Maths-
General
Easy

Question

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

The correct answer is: (n+1)th row in the triangle.


     Step 1 of 2:
    The given expression is open parentheses m squared plus n over 2 close parentheses cubed . Here, the value of n=3 so there are 3+1=4 terms in the expansion of the expression. The values of x equals m squared straight & y equals n over 2 .
    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 open parentheses m squared plus n over 2 close parentheses cubed equals 3 C subscript 0 open parentheses m squared close parentheses cubed plus 3 C subscript 1 open parentheses m squared close parentheses squared open parentheses n over 2 close parentheses plus 3 C subscript 2 open parentheses m squared close parentheses open parentheses n over 2 close parentheses squared plus 3 C subscript 3 open parentheses n over 2 close parentheses cubed end cell row cell equals m to the power of 6 plus 3 open parentheses m to the power of 4 close parentheses open parentheses n over 2 close parentheses plus 3 open parentheses m squared close parentheses open parentheses n squared over 4 close parentheses plus n cubed over 8 end cell row cell equals m to the power of 6 plus fraction numerator 3 m to the power of 4 n over denominator 2 end fraction plus fraction numerator 3 m squared n squared over denominator 4 end fraction plus n cubed over 8 end cell end table
    Thus, the expansion is: open parentheses m squared plus n over 2 close parentheses cubed equals m to the power of 6 plus fraction numerator 3 m to the power of 4 n over denominator 2 end fraction plus fraction numerator 3 m squared n squared over denominator 4 end fraction plus n cubed over 8

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

    Related Questions to study

    General
    Maths-

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

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

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

    Maths-General

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

    General
    Maths-

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

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

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

    Maths-General

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

    General
    Maths-

    Use the binomial theorem to expand the expressions: left parenthesis n plus 5 right parenthesis to the power of 5

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

    Use the binomial theorem to expand the expressions: left parenthesis n plus 5 right parenthesis to the power of 5

    Maths-General

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

    parallel
    General
    Maths-

    Use the binomial theorem to expand the expressions: left parenthesis 2 m plus 2 n right parenthesis to the power of 6

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

    Use the binomial theorem to expand the expressions: left parenthesis 2 m plus 2 n right parenthesis to the power of 6

    Maths-General

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

    General
    Maths-

    Use the binomial theorem to expand the expressions: left parenthesis d minus 3 right parenthesis to the power of 4

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

    Use the binomial theorem to expand the expressions: left parenthesis d minus 3 right parenthesis to the power of 4

    Maths-General

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

    General
    Maths-

    Use the binomial theorem to expand the expressions: open parentheses x cubed plus y squared close parentheses to the power of 6

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

    Use the binomial theorem to expand the expressions: open parentheses x cubed plus y squared close parentheses to the power of 6

    Maths-General

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

    parallel
    General
    Maths-

    Use the binomial theorem to expand the expressions: open parentheses 2 x plus 1 third close parentheses cubed

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n, we would consider the (n+1)th row in the triangle.

    Use the binomial theorem to expand the expressions: open parentheses 2 x plus 1 third close parentheses cubed

    Maths-General

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n, we would consider the (n+1)th row in the triangle.

    General
    Maths-

    Use the binomial theorem to expand the expressions: open parentheses x squared plus 1 close parentheses to the power of 4

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n  , we would consider the (n+1)th row in the triangle.

    Use the binomial theorem to expand the expressions: open parentheses x squared plus 1 close parentheses to the power of 4

    Maths-General

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n  , we would consider the (n+1)th row in the triangle.

    General
    Maths-

    Use the binomial theorem to expand the expressions: left parenthesis b minus 0.5 right parenthesis to the power of 4

    The expansion of (x + y)n  can be also found using the Pascal’s triangle using the (n+1)th row of the triangle.

    Use the binomial theorem to expand the expressions: left parenthesis b minus 0.5 right parenthesis to the power of 4

    Maths-General

    The expansion of (x + y)n  can be also found using the Pascal’s triangle using the (n+1)th row of the triangle.

    parallel
    General
    Maths-

    Use the binomial theorem to expand the expressions: left parenthesis 2 a minus b right parenthesis to the power of 5

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

    Use the binomial theorem to expand the expressions: left parenthesis 2 a minus b right parenthesis to the power of 5

    Maths-General

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

    General
    Maths-

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

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

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

    Maths-General

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

    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.

    parallel
    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.

    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.

    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.