Question

Factorize the following algebraic expression:

$(a^2-5a{)}^2-36$

Answer 1

Given : $(a^2-5a{)}^2-36$
$=(a^2-5a{)}^2-6^2$
Using the formula, $x^2-y^2=(x+y)(x-y)$
$=(a^2-5a+6)(a^2-5a-6)$

Now, factorizing the expression :$(a^2-5a-6)$
On splitting its middle term, we get

$a^2+a-6a-6$
$=a(a+1)-6(a+1)$
$=(a-6)(a+1).....\left(i\right)$

Now, factorizing the expression : $(a^2-5a+6)$
On splitting its middle term, we get

$a^2-2a-3a+6$
$=a(a-2)-3(a-2)$
$=(a-3)(a-2).....\left(ii\right)$

$\therefore (a^2-5a{)}^2-36=(a^2-5a+6\left)\right(a^2-5a-6)$
$=(a+1)(a-6)(a-2)(a-3)$