JAMB 1986 · UME · Q24

Factorize $(4a + 3)^2 - (3a - 2)^2$ .

Worked solution (try it first)

Use the difference of two squares, $A^2 - B^2 = (A - B)(A + B)$ , with $A = 4a + 3$ and $B = 3a - 2$ .
$A - B = 4a + 3 - 3a + 2$ , which is $a + 5$ .
$A + B = 4a + 3 + 3a - 2$ , which is $7a + 1$ .
So the expression is $(a + 5)(7a + 1)$ , option C.