Maths-
General
Easy

Question

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

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 here n ≥ 0 . We are asked to find the expansion of left parenthesis b minus 0.5 right parenthesis to the power of 4 using Binomial theorem.

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


     Step 1 of 2:
    The given expression is left parenthesis b minus 0.5 right parenthesis to the power of 4 . The value of n=4, so the number of terms in the expansion would be 4+1=5 terms. The value of x equals b straight & y equals negative 0.5.
    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 b minus 0.5 right parenthesis to the power of 4 equals 4 C subscript 0 left parenthesis b right parenthesis to the power of 4 plus 4 C subscript 1 left parenthesis b right parenthesis cubed left parenthesis negative 0.5 right parenthesis plus 4 C subscript 2 left parenthesis b right parenthesis squared left parenthesis negative 0.5 right parenthesis squared plus 4 C subscript 3 left parenthesis b right parenthesis to the power of 1 left parenthesis negative 0.5 right parenthesis cubed plus 4 C subscript 4 left parenthesis negative 0.5 right parenthesis to the power of 4 end cell row cell equals b to the power of 4 plus 4 left parenthesis b right parenthesis cubed left parenthesis negative 0.5 right parenthesis plus 6 left parenthesis b right parenthesis squared left parenthesis 0.25 right parenthesis plus 4 b left parenthesis negative 0.125 right parenthesis plus left parenthesis 0.0625 right parenthesis end cell row cell equals b to the power of 4 minus 2 b cubed plus 1.5 b squared minus 0.5 b plus 0.0625 end cell end table
    Thus, the expansion of the expression is left parenthesis b minus 0.5 right parenthesis to the power of 4 equals b to the power of 4 minus 2 b cubed plus 1.5 b squared minus 0.5 b plus 0.0625

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

    Related Questions to study

    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
    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.

    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.

    parallel
    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

    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.

    parallel
    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.

    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.

    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.