Chapter 6, Problem 1RE

To determine

Whether the statement “${\left(2a-3\right)}^2=4a^2-9$” is true or false.

Answer to Problem 1RE

The statement “${\left(2a-3\right)}^2=4a^2-9$” is $\underset{\_}{\text{False}}$.

Explanation of Solution

Expand the expression ${\left(2a-3\right)}^2$ as,

$\begin{array}{c}{\left(2a-3\right)}^2={\left(2a\right)}^2-2\left(2a\right)\left(3\right)+{\left(3\right)}^2\left(\because {\left(a-b\right)}^2=a^2-2ab+b^2\right)\\ =4a^2-12a+9\end{array}$

Thus, the expansion of ${\left(2a-3\right)}^2$ is $4a^2-12a+9$.

Note that as the expansion of ${\left(2a-3\right)}^2$ is $4a^2-12a+9$, the given statement cannot be true.

Therefore, the statement “${\left(2a-3\right)}^2=4a^2-9$” is $\underset{\_}{\text{False}}$.