QUESTION

# Factorize the given equation $36{a^2} - 84ab + 49{b^2}$

Hint: If we observe the given expression the first term and last term are perfect squares. So to simplify we can split them into factors such that factorization of $36{a^2} - 84ab + 49{b^2}$ is easier.
The given expression is $36{a^2} - 84ab + 49{b^2}$.
$\Rightarrow {(6a)^2} - (2 \cdot 6a \cdot 7b) + 7{b^2}$
The above expression is in the form of ${\left( {A - B} \right)^2} = {A^2} - 2AB + {B^2}$,
$\Rightarrow {\left( {6a - 7b} \right)^2}$
$\therefore \left( {6a - 7b} \right)\left( {6a - 7b} \right)$
Note: Factorization is a method of writing numbers as the product of their factors or divisors. We used the identity ${\left( {A - B} \right)^2} = {A^2} - 2AB + {B^2}$, to rewrite the middle term of the given expression and make it into factors.