Maths-
General
Easy

Question

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

hintHint:

The binomial expansion is 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 comma text  here  end text n greater or equal than 0.
We are asked to find the expansion of  left parenthesis x plus 3 right parenthesis cubed using Binomial theorem.

The correct answer is: Pascal’s triangle


     Step 1 of 2:
    The given expression is left parenthesis x plus 3 right parenthesis squared . Here, n=3. So, we would have 3+1=4 terms in the expansion. The value of x equals x straight & y equals 3 .
    Step 2 of 2:
    Substitute the values in the binomial equation to get the expansion:

    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 x plus 3 right parenthesis cubed equals 3 C subscript 0 x cubed plus 3 C subscript 1 left parenthesis x right parenthesis squared left parenthesis 3 right parenthesis plus 3 C subscript 2 left parenthesis x right parenthesis left parenthesis 3 right parenthesis squared plus 3 C subscript 3 left parenthesis 3 right parenthesis cubed end cell row cell equals x cubed plus 3 left parenthesis x right parenthesis squared left parenthesis 3 right parenthesis plus 3 left parenthesis x right parenthesis left parenthesis 9 right parenthesis plus 27 end cell row cell equals x cubed plus 9 x squared plus 27 x plus 27 end cell end table
    Thus, the expansion of the expression is left parenthesis x plus 3 right parenthesis cubed equals x cubed plus 9 x squared plus 27 x plus 27

    The answer can also be found using the Pascal’s triangle (using the fourth row).

    Related Questions to study

    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions : 8 cubed minus 2 cubed

    Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.

    Use polynomial identities to factor the polynomials or simplify the expressions : 8 cubed minus 2 cubed

    Maths-General

    Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.

    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions :
    10 cubed minus 3 cubed

    Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.

    Use polynomial identities to factor the polynomials or simplify the expressions :
    10 cubed minus 3 cubed

    Maths-General

    Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.

    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions :
    10 cubed plus 5 cubed

    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.

    Use polynomial identities to factor the polynomials or simplify the expressions :
    10 cubed plus 5 cubed

    Maths-General

    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.

    parallel
    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions :
    9 cubed plus 6 cubed

    Polynomial identities are used to simplify or to find the product of expressions. It reduces space and time during solving.

    Use polynomial identities to factor the polynomials or simplify the expressions :
    9 cubed plus 6 cubed

    Maths-General

    Polynomial identities are used to simplify or to find the product of expressions. It reduces space and time during solving.

    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions :
    open parentheses 1 over 16 x to the power of 6 minus 25 y to the power of 4 close parentheses

    We can use multiple identities to factorize an expression. Our aim is to reduce the expression into the lowest form.

    Use polynomial identities to factor the polynomials or simplify the expressions :
    open parentheses 1 over 16 x to the power of 6 minus 25 y to the power of 4 close parentheses

    Maths-General

    We can use multiple identities to factorize an expression. Our aim is to reduce the expression into the lowest form.

    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions :
    64 x cubed minus 125 y to the power of 6

    Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.

    Use polynomial identities to factor the polynomials or simplify the expressions :
    64 x cubed minus 125 y to the power of 6

    Maths-General

    Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.

    parallel
    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions :
    216 plus 27 y to the power of 12

    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.

    Use polynomial identities to factor the polynomials or simplify the expressions :
    216 plus 27 y to the power of 12

    Maths-General

    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.

    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions :
    4 x squared minus y to the power of 6

    Polynomial identities are used to simplify or to find the product of expressions. It reduces space and time during solving.

    Use polynomial identities to factor the polynomials or simplify the expressions :
    4 x squared minus y to the power of 6

    Maths-General

    Polynomial identities are used to simplify or to find the product of expressions. It reduces space and time during solving.

    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions : x cubed minus 27 y cubed

    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants

    Use polynomial identities to factor the polynomials or simplify the expressions : x cubed minus 27 y cubed

    Maths-General

    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants

    parallel
    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions : 8 x cubed plus y to the power of 9

    Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.

    Use polynomial identities to factor the polynomials or simplify the expressions : 8 x cubed plus y to the power of 9

    Maths-General

    Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.

    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions : x9 - 8

    Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions

    Use polynomial identities to factor the polynomials or simplify the expressions : x9 - 8

    Maths-General

    Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions

    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions : x8 - 9

    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.

    Use polynomial identities to factor the polynomials or simplify the expressions : x8 - 9

    Maths-General

    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.

    parallel
    General
    Maths-

    Use polynomial identities to multiply the expressions ? open parentheses 25 x squared minus 15 y squared close parentheses open parentheses 25 x squared plus 15 y squared close parentheses

    Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.

    Use polynomial identities to multiply the expressions ? open parentheses 25 x squared minus 15 y squared close parentheses open parentheses 25 x squared plus 15 y squared close parentheses

    Maths-General

    Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.

    General
    Maths-

    Use polynomial identities to multiply the expressions ? open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses

    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.

    Use polynomial identities to multiply the expressions ? open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses

    Maths-General

    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.

    General
    Maths-

    Use polynomial identities to multiply the expressions ? (10 + 21)2

    Algebraic expression is an expression that is built by the combination of integer constants and variables.

    Use polynomial identities to multiply the expressions ? (10 + 21)2

    Maths-General

    Algebraic expression is an expression that is built by the combination of integer constants and variables.

    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.