Maths-
General
Easy

Question

Expand left parenthesis 3 x plus 4 y right parenthesis cubed using Pascal’s triangle.

hintHint:

Pascal's Triangle is a method to know the binomial coefficients of terms of binomial expression (x + y)n , where n can be any positive integer and x, y are real numbers. Pascal Triangle is represented in a triangular form, it is kind of a number pattern in the form of a triangular arrangement.
We are asked to find the expansion of left parenthesis 3 x plus 4 y right parenthesis cubed using the Pascal’s triangle.

The correct answer is: binomial theorem


     Step 1 of 2:
    The given expression is left parenthesis 3 x plus 4 y right parenthesis cubed . Here, n=3. Thus, the number of terms in the expansion would be n+1=3+1=4. We have to fourth line of the pascal’s triangle to get the coefficients.
    Step 2 of 2:


    Thus, analyzing the figure, we get the expansion of left parenthesis 3 x plus 4 y right parenthesis cubed as

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell left parenthesis 3 x plus 4 y right parenthesis cubed equals 1 left parenthesis 3 x right parenthesis cubed plus 3 left parenthesis 3 x right parenthesis squared left parenthesis 4 y right parenthesis plus 3 left parenthesis 3 x right parenthesis left parenthesis 4 y right parenthesis squared plus 1 left parenthesis 4 y right parenthesis cubed end cell row cell equals 27 x cubed plus 3 open parentheses 9 x squared close parentheses left parenthesis 4 y right parenthesis plus 3 left parenthesis 3 x right parenthesis open parentheses 16 y squared close parentheses plus 64 y cubed end cell row cell equals 27 x cubed plus 108 x squared y plus 144 x y squared plus 64 y cubed end cell end table
    Hence, the expansion is, left parenthesis 3 x plus 4 y right parenthesis cubed equals 27 x cubed plus 108 x squared y plus 144 x y squared plus 64 y cubed.

    The answer can be found using the binomial theorem left parenthesis x plus y right parenthesis to the power of n equals sum from k equals 0 to n of   n C subscript k x to the power of n minus k end exponent y to the power of k text  where  end text n greater or equal than 0

    Related Questions to study

    General
    Maths-

    Use binomial theorem to expand expression (x + y)7 .

    The answer can be found using the Pascal’s triangle. For an expression (x + y)n , we would have n + 1 term.

    Use binomial theorem to expand expression (x + y)7 .

    Maths-General

    The answer can be found using the Pascal’s triangle. For an expression (x + y)n , we would have n + 1 term.

    General
    Maths-

    Use binomial theorem to expand expression (d - 1)4

    The answer can be found using the Pascal’s triangle. For an expression left parenthesis x plus y right parenthesis to the power of n , we would have n+ 1 term.

    Use binomial theorem to expand expression (d - 1)4

    Maths-General

    The answer can be found using the Pascal’s triangle. For an expression left parenthesis x plus y right parenthesis to the power of n , we would have n+ 1 term.

    General
    Maths-

    Use Pascal triangle to expand the expression (a - b)6 .

    The answer can be found using the binomial expansion of left parenthesis x plus y right parenthesis to the power of n equals sum from k equals 0 to n of   n C subscript k x to the power of n minus k end exponent y to the power of k text  where  end text n greater or equal than 0

    Use Pascal triangle to expand the expression (a - b)6 .

    Maths-General

    The answer can be found using the binomial expansion of left parenthesis x plus y right parenthesis to the power of n equals sum from k equals 0 to n of   n C subscript k x to the power of n minus k end exponent y to the power of k text  where  end text n greater or equal than 0

    parallel
    General
    Maths-

    Use Pascal’s triangle to expand the expression (x + 1)5

    The answer can be found using the binomial expansion of left parenthesis x plus y right parenthesis to the power of n equals sum from k equals 0 to n of   n C subscript k x to the power of n minus k end exponent y to the power of k text  where  end text n greater or equal than 0

    Use Pascal’s triangle to expand the expression (x + 1)5

    Maths-General

    The answer can be found using the binomial expansion of left parenthesis x plus y right parenthesis to the power of n equals sum from k equals 0 to n of   n C subscript k x to the power of n minus k end exponent y to the power of k text  where  end text n greater or equal than 0

    General
    Maths-

    How many terms will there be in the expansion of the expressionleft parenthesis x plus 3 right parenthesis to the power of n . Explain how you know?

    How many terms will there be in the expansion of the expressionleft parenthesis x plus 3 right parenthesis to the power of n . Explain how you know?

    Maths-General
    General
    Maths-

    Find the third term of the binomial expansion left parenthesis a minus 3 right parenthesis to the power of 6

    The expansion of (x + y)n has n+1 terms while expanding. The answer can be found using the Pascal’s triangle or binomial expansion.

    Find the third term of the binomial expansion left parenthesis a minus 3 right parenthesis to the power of 6

    Maths-General

    The expansion of (x + y)n has n+1 terms while expanding. The answer can be found using the Pascal’s triangle or binomial expansion.

    parallel
    General
    Chemistry-

    Factor open parentheses x cubed minus 125 y to the power of 6 close parentheses in the form left parenthesis x minus a right parenthesis open parentheses x squared plus b x plus c close parentheses . Then find the value of a,b and c.

    Factor open parentheses x cubed minus 125 y to the power of 6 close parentheses in the form left parenthesis x minus a right parenthesis open parentheses x squared plus b x plus c close parentheses . Then find the value of a,b and c.

    Chemistry-General
    General
    Maths-

    Find the fifth term of the binomial expansion left parenthesis x plus y right parenthesis to the power of 5

    The expansion of left parenthesis x plus y right parenthesis to the power of n has n+1 terms while expanding. The answer can be found using the Pascal’s triangle or binomial expansion.

    Find the fifth term of the binomial expansion left parenthesis x plus y right parenthesis to the power of 5

    Maths-General

    The expansion of left parenthesis x plus y right parenthesis to the power of n has n+1 terms while expanding. The answer can be found using the Pascal’s triangle or binomial expansion.

    General
    Maths-

    The sum of the coefficients in the expansion of the expression left parenthesis a plus b right parenthesis to the power of n is 64. Use Pascal’s triangle to find the value of n.

    Using Pascal's Triangle, where n can be any positive integer as x and y are real numbers, one can determine the binomial coefficients of the terms of the binomial formula (x + y)n. Pascal Triangle is a type of number pattern that appears as a triangular arrangement and is represented by triangles. It starts with '1' at the top and continues with '1' on the triangle's two sides. Each new number in the Pascal triangle has equal values to the sum of the two integers above and below. The probability conditions in which this triangle is utilized vary. Every row represents this table's coefficient of expansion of (x + y)n. Zero row n = 0, (x + y)0

    The sum of the coefficients in the expansion of the expression left parenthesis a plus b right parenthesis to the power of n is 64. Use Pascal’s triangle to find the value of n.

    Maths-General

    Using Pascal's Triangle, where n can be any positive integer as x and y are real numbers, one can determine the binomial coefficients of the terms of the binomial formula (x + y)n. Pascal Triangle is a type of number pattern that appears as a triangular arrangement and is represented by triangles. It starts with '1' at the top and continues with '1' on the triangle's two sides. Each new number in the Pascal triangle has equal values to the sum of the two integers above and below. The probability conditions in which this triangle is utilized vary. Every row represents this table's coefficient of expansion of (x + y)n. Zero row n = 0, (x + y)0

    parallel
    General
    Maths-

    A student says that the expansion of the expression left parenthesis negative 4 y plus z right parenthesis to the power of 7has seven terms. Describe and correct
    the error the student may have made ?

    A student says that the expansion of the expression left parenthesis negative 4 y plus z right parenthesis to the power of 7has seven terms. Describe and correct
    the error the student may have made ?

    Maths-General
    General
    Maths-

    Expand the expression left parenthesis 2 x minus 1 right parenthesis to the power of 4 .what is the sum of the coefficients?

    Expand the expression left parenthesis 2 x minus 1 right parenthesis to the power of 4 .what is the sum of the coefficients?

    Maths-General
    General
    Maths-

    Use Pascal’s triangle and the binomial theorem to expand left parenthesis x plus 1 right parenthesis to the power of 4 . Justify your work.

    Use Pascal’s triangle and the binomial theorem to expand left parenthesis x plus 1 right parenthesis to the power of 4 . Justify your work.

    Maths-General
    parallel
    General
    Maths-

    Emma factored  open parentheses 625 g to the power of 16 minus 25 h to the power of 4 close parenthesesDescribe and correct the error Emma made in factoring the polynomial.

    A polynomial is factored when expressed as the product of more than one factor; this is somewhat the opposite of multiplying. The following properties or identities, along with other methods, are typically used to factor polynomials.
    ¶A number is quickly factorized into smaller digits or factors of the number using the factorization formula. Finding the zeros of the polynomial expression or the values of the variables in the given expression are both made possible by factoring polynomials.
    ¶There are many ways to factorize a polynomial of the form axn + bxn - 1 + cxn - 2+ ........., px + q, including grouping, using identities, and substituting.

    Emma factored  open parentheses 625 g to the power of 16 minus 25 h to the power of 4 close parenthesesDescribe and correct the error Emma made in factoring the polynomial.

    Maths-General

    A polynomial is factored when expressed as the product of more than one factor; this is somewhat the opposite of multiplying. The following properties or identities, along with other methods, are typically used to factor polynomials.
    ¶A number is quickly factorized into smaller digits or factors of the number using the factorization formula. Finding the zeros of the polynomial expression or the values of the variables in the given expression are both made possible by factoring polynomials.
    ¶There are many ways to factorize a polynomial of the form axn + bxn - 1 + cxn - 2+ ........., px + q, including grouping, using identities, and substituting.

    General
    Maths-

    Expand left parenthesis 3 x plus 4 y right parenthesis cubed using binomial theorem.

    Expand left parenthesis 3 x plus 4 y right parenthesis cubed using binomial theorem.

    Maths-General
    General
    Maths-

    If an event has a probability of success p and a probability of failure q , then each term inthe expansion of(p+q)n represents a probability. For example , if a basketball player makes 60% of his free throw attempts , p= 0.6 and q= 0.4. To find the probability the basketball player will make exactly h out of k free throws, find straight C subscript straight k minus straight h end subscript straight p to the power of straight h straight q to the power of straight k minus straight h end exponent where C subscript k minus h end subscript a a coefficient of row k of Pascal’s triangle is, p is the probability of success, and q is the probability of failure.

    If an event has a probability of success p and a probability of failure q , then each term inthe expansion of(p+q)n represents a probability. For example , if a basketball player makes 60% of his free throw attempts , p= 0.6 and q= 0.4. To find the probability the basketball player will make exactly h out of k free throws, find straight C subscript straight k minus straight h end subscript straight p to the power of straight h straight q to the power of straight k minus straight h end exponent where C subscript k minus h end subscript a a coefficient of row k of Pascal’s triangle is, p is the probability of success, and q is the probability of failure.

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.