Question

Factorize:
$63{a^2} - 112{b^2}$
$\left( A \right)\,\,7\left( {3a - b} \right)\left( {a - 4b} \right)$
$\left( B \right)\,\,7\left( {3a + 4b} \right)\left( {3a - 4b} \right)$
$\left( C \right)\,\,\left( {3a - 4b} \right)\left( {3a - 4b} \right)$
$\left( D \right)\,\left( {3a + 4b} \right)\left( {3a - 4b} \right)$

Answer 1

Hint: This question is nothing but just an application of a single formula of algebra. It would become very easy if you identify how we have to apply the formula in this question because the numerical part is not a perfect square. Factorization is a process in which we find the roots of a given equation.
Formula used: ${m^2} - {n^2} = \left( {m + n} \right)\left( {m - n} \right)$

Complete step-by-step answer:
In the given question, we have
$ \Rightarrow 63{a^2} - 112{b^2}$
Taking $7$ common
$ \Rightarrow 7\left( {9{a^2} - 16{b^2}} \right)$
Now,
We can also write ${\left( {3a} \right)^2} = 9{a^2}\,\,and\,\,{\left( {4a} \right)^2} = 16{b^2}$
$ \Rightarrow 7\left( {{{\left( {3a} \right)}^2} - {{\left( {4b} \right)}^2}} \right)$
Now, using the formula ${m^2} - {n^2} = \left( {m + n} \right)\left( {m - n} \right)$
$ \Rightarrow 7\left( {3a + 4b} \right)\left( {3a - 4b} \right)$
So, the correct answer is “Option B”.

Note: While doing factorization one must know all the formulas in algebra regarding square and cube of numbers. Factoring an algebraic expression means writing the expression as a product of factors.
To verify whether the factors are correct or not, multiply them and check if you get the original algebraic expression. An algebraic expression can be factored using the common factor method, regrouping like terms together, and also by using algebraic identities.