Question

Factorize the following expressions:
$2a^5{b}^3-14a^2{b}^2+4a^{3}b$

Answer 1

Let us first find the HCF of all the terms of the given polynomial $2a^5{b}^3-14a^2{b}^2+4a^{3}b$ by factoring the terms as follows:

$2a^5{b}^3=2\times a\times a\times a\times a\times a\times b\times b\times b14a^2{b}^2=2\times 7\times a\times a\times b\times b4a^{3}b=2\times 2\times a\times a\times a\times b$

Therefore, $HCF=2\times a\times a\times b=2a^{2}b$

Now, we factor out the HCF from each term of the polynomial $2a^5{b}^3-14a^2{b}^2+4a^{3}b$ as shown below:

$2a^5{b}^3-14a^2{b}^2+4a^{3}b=2a^{2}b(a^3{b}^2-7b+2a)$

Hence, $2a^5{b}^3-14a^2{b}^2+4a^{3}b=2a^{2}b(a^3{b}^2-7b+2a)$.