Question

Work with your group to find the following quotients. (a) x^3- a^3 ÷ x-a (b) x^4- a^4 ÷ x-a

Answer 1

(a)
`a^2+ab+b^2`

(b)
`(x+a)(x^2+a^2)`

Explanation:

We have given expression

(a)
`(x^3-a^3)/(x-a)`

We have to find the quotient

From algebraic identity we know that

`a^3-b^3=(a-b)(a^2+ab+b^2)`

So
`(x^3-a^3)/(x-a)=((a-b)(a^2+ab+b^2))/(a-b)=a^2+ab+b^2`

(b) We have given
`(x^4-a^4)/(x-a)`

We know the algebraic identity

`a^2-b^2=(a+b)(a-b)`

`(x^4-a^4)/(x-a)=((x^2)^2-(a^2)^2)/(x-a)=((x^2-a^2)(x^2+a^2))/(x-a)=((x+a)(x-a)(x^2+a^2))/(x-a)=(x+a)(x^2+a^2)`