Question

Factorise.
$\left(i\right)a^4-b^4\left(ii\right)p^4-81\left(iii\right)x^4-{\left(y+z\right)}^4$
$\left(iv\right)x^4-{\left(x-z\right)}^4\left(v\right)a^4-2a^2{b}^2+b^4$

Answer 1

Factorise

(i) $a^4-b^4=(a^2{)}^2-(b^2{)}^2$

It is in the form of $a^2-b^2=(a+b)(a-b)$

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

(ii) $p^4-81=(p^2{)}^2-(3^2{)}^2$

$=(p^2+3^2)(p^2-3^2)$

(iii) $x^4-(y+z{)}^4=(x^2{)}^2-(y+z^2{)}^2$

$(x^2+(y+z{)}^2\left)\right(x^2-(y+z{)}^2)$

(iv) $x^4-(x-z{)}^4=(x^2{)}^2-(x-z^2{)}^2$

$=(x^2+(x-z{)}^2(x^2-(x-z{)}^2)$

(v) $a^4-2a^2{b}^2+b^4=$

It is in the form of $a^2-2ab+b^2=(a-b{)}^2$

$=(a^2{)}^2-2.a^2.b^2+(b^2{)}^2$

$=(a^2-b^2{)}^2$.