Question

Factorize The following expression:
$4{{a}^{2}}-8ab$.

Answer 1

Hint: Here, we may first find what is the common factor between the two terms in the given expression i.e. between $4{{a}^{2}}$ and $8ab$. After finding the common term we may take out this common term and hence factorize the given expression.

Complete step-by-step answer:
We know that factorization is breaking an entity into a product of another entity.
So, in this case we may apply this method of factorization to simplify the given expression.
Since, the given expression is:
$4{{a}^{2}}-8ab$
In this expression we have two terms, first one is $4{{a}^{2}}$ and second one is $-8ab$.
So, we may factorize both the terms individually. So, first of all we take $4{{a}^{2}}$ and we can write it as:
$4{{a}^{2}}=4\times a\times a...........(1)$
Also, we can write the second term $-8ab$ as:
$-8ab=-8\times a\times b$
Now, we will try to find whether there is any common factor between $4{{a}^{2}}$ and $-8ab$.
We can see that, $-8ab$ can also be written as:
$-8ab=-4\times 2\times a\times b.........(2)$
Now on comparing equation (1) and equation (2), we get that 4a is the common factor between the two terms. So, we can take 4a common from both the terms in this expression, and get:
$\begin{align}
  & 4\times a\times a-4\times 2\times a\times b \\
 & =4a\left( a-2b \right) \\
\end{align}$
Hence, on factorizing the given expression $4{{a}^{2}}-8ab$, we get $4a\left( a-2b \right)$.

Note: Students should note here that while factoring any expression, the sign of the terms should always be considered. Otherwise, while taking any common term and not taking care of signs there are chances of mistakes.