JAMB 2017 · UTME (set 2) · Q46

Quadratics & their graphs

Factorize completely $x^2 + 2xy + y^2 + 3x + 3y - 18$ .

Worked solution (try it first)

The first three terms are a perfect square: $x^2 + 2xy + y^2 = (x + y)^2$ .
The next two are $3(x + y)$ .
Let $u = x + y$ .
The expression is $u^2 + 3u - 18$ .
Find two numbers with product $-18$ and sum 3: they are 6 and $-3$ .
So $u^2 + 3u - 18 = (u + 6)(u - 3)$ .
Put back $u = x + y$ : $(x + y + 6)(x + y - 3)$ , option A.

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