Answer:
(a) [tex]a^2+ab+b^2[/tex]
(b) [tex](x+a)(x^2+a^2)[/tex]
Step-by-step explanation:
We have given expression
(a) [tex]\frac{x^3-a^3}{x-a}[/tex]
We have to find the quotient
From algebraic identity we know that
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
So [tex]\frac{x^3-a^3}{x-a}=\frac{(a-b)(a^2+ab+b^2)}{a-b}=a^2+ab+b^2[/tex]
(b) We have given [tex]\frac{x^4-a^4}{x-a}[/tex]
We know the algebraic identity
[tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]\frac{x^4-a^4}{x-a}=\frac{(x^2)^2-(a^2)^2}{x-a}=\frac{(x^2-a^2)(x^2+a^2)}{x-a}=\frac{(x+a)(x-a)(x^2+a^2)}{x-a}=(x+a)(x^2+a^2)[/tex]
