Question

The factorisation of $a^6+b^6$ is equal to .

• A. $(a^2+b^2)(a^4-a^2{b}^2+b^4)$
• B. $(a^2+b^2)(a^4+a^2{b}^2+b^4)$
• C. $(a^2-b^2)(a^4+a^2{b}^2+b^4)$
• D. $(a^2-b^2)(a^4+a^2{b}^2+b^4)$

Answer 1

The correct option is B $(a^2+b^2)(a^4+a^2{b}^2+b^4)$

The given expression is $a^6+b^6$
This can be written as $(a^2{)}^3+(b^2{)}^3$
= $(a^2+b^2)\left[\right(a^2{)}^2+a^2{b}^2+\left(b^2{)}^2\right)$ ....[$a^3+b^3=(a+b)(a^2-ab+b^2)$]
= $(a^2+b^2)(a^4+a^2{b}^2+b^4)$