Question

Factorize the given equation \[36{a^2} - 84ab + 49{b^2}\]

Answer 1

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.

Complete step-by-step answer:
The given expression is \[36{a^2} - 84ab + 49{b^2}\].
Since the first term and last term in the expression are perfect squares,
Converting the whole expression into a form like
\[ \Rightarrow {(6a)^2} - (2 \cdot 6a \cdot 7b) + 7{b^2}\]
The above expression is in the form of \[{\left( {A - B} \right)^2} = {A^2} - 2AB + {B^2}\],
\[ \Rightarrow {\left( {6a - 7b} \right)^2}\]
We found the factorization,
\[\therefore \left( {6a - 7b} \right)\left( {6a - 7b} \right)\]

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.