Question
Factorize the following expressions:
$x^6+y^6$
$x^6+y^6$
✓
Answer
$=\left(x^2\right)^3+\left(y^2\right)^3$
$\left.=\left(x^2+y^2\right)\left(x^2\right)^2-x^2 y^2+\left(y^2\right)^2\right)$
$=\left(x^2+y^2\right)\left(x^4-x^2 y^2+y^4\right)\left[\therefore a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]$
$\therefore x^6+y^6=\left(x^2+y^2\right)\left(x^4-x^2 y^2+y^4\right)$
$\left.=\left(x^2+y^2\right)\left(x^2\right)^2-x^2 y^2+\left(y^2\right)^2\right)$
$=\left(x^2+y^2\right)\left(x^4-x^2 y^2+y^4\right)\left[\therefore a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]$
$\therefore x^6+y^6=\left(x^2+y^2\right)\left(x^4-x^2 y^2+y^4\right)$
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