Chapter 1.1, Problem 1AGP

To determine

To Simplify : The expression $16u^2-3$

Answer to Problem 1AGP

  $\left(4u+\sqrt{3}\right)\left(4u-\sqrt{3}\right)$

Explanation of Solution

Given information :

The expression $16u^2-3$

Calculation :

The expression $16u^2-3$ can be written as follows

  $\begin{array}{c}16u^2-3=4^2{u}^2-{\left(\sqrt{3}\right)}^2\\ ={\left(4u\right)}^2-{\left(\sqrt{3}\right)}^2\end{array}$

Hence, $16u^2-3={\left(4u\right)}^2-{\left(\sqrt{3}\right)}^2$

Use the formula $a^2-b^2=\left(a+b\right)\left(a-b\right)$

Here, $a=4u\text{ and }b=\sqrt{3}$

  ${\left(4u\right)}^2-{\left(\sqrt{3}\right)}^2=\left(4u+\sqrt{3}\right)\left(4u\sqrt{3}\right)$