Give possible expressions for the length and breadth of the rectangle whose area is given by $4 a^{2}+4 a-3$

Area: $4 a^{2}+4 a-3$

Using the method of splitting the middle term, we first two numbers whose sum is +4 and produce is $4 \times(-3)=-12$

Now, $+6-2=+4$ and $(+6) \times(-2)=-12$

We split the middle term $4 a$ as $4 a=+6 a-2 a$,

So, that $4 a+4 a-3=4 a^{2}+6 a-2 a-3$

$=2 a(2 a+3)-1(2 a+3)$

$=(2 a-1)(2 a+3)$

Now, area of rectangle $=4 a^{2}+4 a-3$

Also, area of rectangle = length $\times$ breadth and $4 a^{2}+4 a-3=(2 a-1)(2 a+3)$

So, the possible expressions for the length and breadth of the rectangle are length $=(2 a-1)$ and breadth $=(2 a+3)$ or, length $=(2 a+3)$ and breadth $=(2 a-1)$