Question
Factorise:
$x^4-625$
$x^4-625$
✓
Answer
$x^4-625$
$=\left(x^2\right)^2-(25)^2$
$=\left(x^2+25\right)\left(x^2-25\right)$
$=\left(x^2+25\right)\left(x^2-5^2\right)\left[\therefore a^2-b^2=(a-b)(a+b)\right]$
$=\left(x^2+25\right)(x+5)(x-5)$
$=\left(x^2\right)^2-(25)^2$
$=\left(x^2+25\right)\left(x^2-25\right)$
$=\left(x^2+25\right)\left(x^2-5^2\right)\left[\therefore a^2-b^2=(a-b)(a+b)\right]$
$=\left(x^2+25\right)(x+5)(x-5)$
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