Question

How do you solve $q^2+11qr+18r^2$?

Answer 1

Solve the given expression.

Given: $q^2+11qr+18r^2$

Here we can split the middle term of the given equation as $11qr=9qr+2qr$

So, the given expression becomes,

$q^2+11qr+18r^2$$=q^2+9qr+2qr+18r^2$

$\Rightarrow$$q^2+11qr+18r^2=$$q(q+9r)+2r(q+9r)$

$\Rightarrow$$q^2+11qr+18r^2=$$(q+2r)(q+9r)$

To solve the expression, it needs to be equated to $0$

$\Rightarrow$$(q+2r)(q+9r)=0$

$\Rightarrow$$q+2r=0,q+9r=0$

$\Rightarrow$$q=-2r,-9r$

Hence, the required solution is $q=-2r,-9r$.