Question

How do you factorize \[4{{x}^{2}}-64{{y}^{2}}\] ?

Answer 1

Hint: In order to factorize the above algebraic expression given in the question we will use algebraic identities. First, we will check whether the given algebraic expression can be factorized using identities. since the above equation is similar to one identity. Therefore, we will simplify it using the algebraic identity and thus get the factors.

Complete step by step answer:
The above question belongs to the concept of factorization. In basic terms factorization is writing a number as a product of several factors. In factorization w check for common factors. In others words factorization is the process of finding two or more expressions whose product is the given expression.
Now in the given question we have \[4{{x}^{2}}-64{{y}^{2}}\] . we will use basic algebraic identity to factorize it.
We know that \[{{x}^{2}}-{{y}^{2}}=(x+y)(x-y)\] is an algebraic identity. We will convert the given expression into this form.
Thus, we will get
\[\begin{align}
  & 4{{x}^{2}}-64{{y}^{2}} \\
 & \Rightarrow {{(2x)}^{2}}-{{(8y)}^{2}} \\
\end{align}\]
Now applying the identity on the above equation.
\[\Rightarrow {{(2x)}^{2}}-{{(8y)}^{2}}=(2x+8y)(2x-8y)\]
This means \[(2x+8y)\] and \[(2x-8y)\] are the factors of the given algebraic expression.
Thus, after factorization of \[4{{x}^{2}}-64{{y}^{2}}\] we get \[(2x+8y)(2x-8y)\].

Note: Factorization of algebraic expression using identities is a bit tricky therefore perform all the steps carefully in order to avoid mistakes. Remember that there is no “sum of squares “factoring formula. Keep in mind the identities used in the above question. Do not skip steps while factorization and always mention the identity used.