Question

Factorize:
$9c-a^2+4ab-4b^2$

Answer 1

Given expression is $9c-a^2+4ab-4b^2$.

We can write it as:

$9c-(a^2-4ab+4b^2)$

Using the property $(a-b{)}^2=a^2-2ab+b^2$, we can write $a^2-4ab+4b^2$ as $(a-2b{)}^2$

Hence, the expression becomes,

$9c-(a-2b{)}^2$

$\Rightarrow (3\sqrt{c}{)}^2-(a-2b{)}^2$

Now, using the property $a^2-b^2=(a+b)(a-b)$, the expression can be written as:

$[3\sqrt{c}+a-2b][3\sqrt{c}-a+2b]$

Hence, $9c-a^2+4ab-4b^2=[3\sqrt{c}+a-2b][3\sqrt{c}-a+2b]$.