Question

Factorise $10000-x^4$ is ____

• A. $(10-x)(x+10)(x^2+100)$
• B. $(10-2x)(2x+10)(x^2+100)$
• C. $(x-99)(x+99)(2x^2+100)$
• D. $(x-100)(x+100)(x^2+99)$

Answer 1

The correct option is A $(10-x)(x+10)(x^2+100)$

$10000-x^4$
We know $a^2-b^2=(a+b)(a-b)$
$10000-x^4=({10}^2{)}^2-(x^2{)}^2$
Now, let $x^2=k$
$({10}^2{)}^2-(x^2{)}^2=(100{)}^2-(k{)}^2=(k+100)(100-k)$
$(k+100)(100-k)=(x^2+{10}^2)({10}^2-x^2)$
Factorising further ,we have
$(x^2+{10}^2)({10}^2-x^2)=(x^2+100)(10+x)(10-x)$