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if $a=2x-3$, $b=2x+5$ and $x=2$, find the product of $a$ and $b$ by using formulae.

Welcome to BdMO Online Forum. Let me answer it since nobody is doing so.

Suppose $m=2x+1$. The product becomes $\begin{align*}(m+4)(m-4) &=m^2-16\\
&=(2x+1)^2-16\\
&=4x^2+4x-15
\end{align*}$
Now setting $x=2$, we get $16+8-15=9$

The product of $a$ and $b$ is,
\[\begin{split}
a\times b &= (2x-3)(2x+5)\\
&= \{2x+(-3)\}(2x+5)\\
&= (2x)(2x)+(5-3)2x-15\\
&= 16+8-15\\
&= 9
\end{split}\]