Simplify each of the following products:
$ (\frac{1}{2} a-3 b)(3 b+\frac{1}{2} a)(\frac{1}{4} a^{2}+9 b^{2}) $

Given:

\( (\frac{1}{2} a-3 b)(3 b+\frac{1}{2} a)(\frac{1}{4} a^{2}+9 b^{2}) \)

To do:

We have to simplify the given product.

Solution:

We know that,

$(a+b)^2=a^2+b^2+2ab$

$(a-b)^2=a^2+b^2-2ab$

$(a+b)(a-b)=a^2-b^2$

Therefore,

$(\frac{1}{2} a-3 b)(3 b+\frac{1}{2} a)(\frac{1}{4} a^{2}+9 b^{2})=(\frac{1}{2} a-3 b)(\frac{1}{2} a+3 b)(\frac{1}{4} a^{2}+9 b^{2})$

$={(\frac{1}{2} a)^{2}-(3 b)^{2}}(\frac{1}{4} a^{2}+9 b^{2})$

$=(\frac{1}{4} a^{2}-9 b^{2})(\frac{1}{4} a^{2}+9 b^{2})$

$=(\frac{1}{4} a^{2})^{2}-(9 b^{2})^{2}$

$=\frac{1}{16} a^{4}-81 b^{4}$

Hence, $(\frac{1}{2} a-3 b)(3 b+\frac{1}{2} a)(\frac{1}{4} a^{2}+9 b^{2})=\frac{1}{16} a^{4}-81 b^{4}$.

Tutorialspoint

e

Updated on: 10-Oct-2022

28 Views

Kickstart Your Career

Get certified by completing the course

Get Started