FACTORISATION

The trick in such examples is to transform or identify the hidden quadratic equation, then find it's root.

The procedure is illustrated below.

1/  5(3x + y)² + 6(3x + y) - 8

Let (3x + y) = X

5X² + 6X - 8

Roots of this quadratic equation are,

X =[-6±(36+160)]/10

The roots are, -2 and 4/5,

Hence,

(X+2)(X-4/5) =

(3x + y + 2)(3x + y - 4/5)

Hence, factorization of,

5(3x + y)² + 6(3x + y) - 8 is,

(3x + y + 2)(3x + y - 4/5).

Similarly other two can be solved.

Regards,

Team,

TopperLearning.