Maths-
General
Easy

Question

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

The correct answer is: Hence, the expansion is,


    ANSWER:
    Hint:
    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 cubedusing the Pascal’s triangle.
    Step 1 of 2:
    The given expression isleft 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:
    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
    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
    equals 27 x cubed plus 108 x squared y plus 144 x y squared plus 64 y cubed
    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
    Note:
    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 kwhere n greater or equal than 0 .

    Related Questions to study

    General
    Maths-

    How many terms are there in the expansion of left parenthesis 2 x plus 7 y right parenthesis to the power of 9

    How many terms are there in the expansion of left parenthesis 2 x plus 7 y right parenthesis to the power of 9

    Maths-General
    General
    Maths-

    A Pythagorean triple is a set of three positive integers a, b and c that satisfy a squared plus b squared equals c squared. The Identity open parentheses straight x squared minus straight y squared close parentheses squared plus left parenthesis 2 xy right parenthesis squared equals open parentheses straight x squared plus straight y squared close parentheses squared can be used to generate Pythagorean triples. Use the identity to generate a Pythagorean triple when x = 5 and y = 4

    A Pythagorean triple is a set of three positive integers a, b and c that satisfy a squared plus b squared equals c squared. The Identity open parentheses straight x squared minus straight y squared close parentheses squared plus left parenthesis 2 xy right parenthesis squared equals open parentheses straight x squared plus straight y squared close parentheses squared can be used to generate Pythagorean triples. Use the identity to generate a Pythagorean triple when x = 5 and y = 4

    Maths-General
    General
    Maths-

    Use binomial theorem to expand expressionleft parenthesis x plus y right parenthesis to the power of 7.

    Use binomial theorem to expand expressionleft parenthesis x plus y right parenthesis to the power of 7.

    Maths-General
    parallel
    General
    Maths-

    Use binomial theorem to expand expression left parenthesis d minus 1 right parenthesis to the power of 4

    Use binomial theorem to expand expression left parenthesis d minus 1 right parenthesis to the power of 4

    Maths-General
    General
    Maths-

    The dimensions of a rectangle are shown. Write the area of the rectangle as a sum of cubes .

    The dimensions of a rectangle are shown. Write the area of the rectangle as a sum of cubes .

    Maths-General
    General
    Maths-

    Use Pascal triangle to expand the expression left parenthesis a minus b right parenthesis to the power of 6.

    Use Pascal triangle to expand the expression left parenthesis a minus b right parenthesis to the power of 6.

    Maths-General
    parallel
    General
    Maths-

    A Medium sized Shipping box with side length s units has a volume of S cubed cubic units.
    a. A Large shipping box has side lengths that are 3 units longer than the medium shipping box. Write a binomial expression for the volume of the large shipping box .
    b. Expand the polynomial in part A to simplify the volume of the large shipping box ?

    A Medium sized Shipping box with side length s units has a volume of S cubed cubic units.
    a. A Large shipping box has side lengths that are 3 units longer than the medium shipping box. Write a binomial expression for the volume of the large shipping box .
    b. Expand the polynomial in part A to simplify the volume of the large shipping box ?

    Maths-General
    General
    Maths-

    Use Pascal’s triangle to expand the expression left parenthesis x plus 1 right parenthesis squared

    Use Pascal’s triangle to expand the expression left parenthesis x plus 1 right parenthesis squared

    Maths-General
    General
    Maths-

    Use the binomial theorem to expand the expressions:
    open parentheses straight m squared plus straight n over 2 close parentheses cubed

    Use the binomial theorem to expand the expressions:
    open parentheses straight m squared plus straight n over 2 close parentheses cubed

    Maths-General
    parallel
    General
    Maths-

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

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

    Maths-General
    General
    Maths-

    Use the binomial theorem to expand the expressions:
    left parenthesis 4 straight g plus 2 straight h right parenthesis to the power of 4

    Use the binomial theorem to expand the expressions:
    left parenthesis 4 straight g plus 2 straight h right parenthesis to the power of 4

    Maths-General
    General
    Maths-

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

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

    Maths-General
    parallel
    General
    Maths-

    Use polynomial identities to factor each polynomial :
    m to the power of 9 plus 27 n to the power of 6

    Use polynomial identities to factor each polynomial :
    m to the power of 9 plus 27 n to the power of 6

    Maths-General
    General
    Maths-

    Use the binomial theorem to expand the expressions:
    left parenthesis 3 x minus 0.2 right parenthesis cubed

    Use the binomial theorem to expand the expressions:
    left parenthesis 3 x minus 0.2 right parenthesis cubed

    Maths-General
    General
    Maths-

    Use polynomial identities to factor each polynomial :
    open parentheses 8 x to the power of 6 minus y cubed close parentheses

    Use polynomial identities to factor each polynomial :
    open parentheses 8 x to the power of 6 minus y cubed close parentheses

    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.