EDGE Math 8

Factoring Other Trinomials

Trinomials in the Form $x^{2} + (a + b) x + a b$

The previously presented factoring technique can be extended to trinomials in the form $x^{2} + (a + b) x y + a b y^{2} .$ Its factored form is shown below.

x^{2} + (a + b) x y + a b y^{2}

= (x + a y) (x + b y)

Example

Factor each trinomial.

a^{2} + 11 a b + 18 b^{2}

b^{2} - 2 b z - 24 z^{2}

x^{2} - 17 x y + 60 y^{2}

r^{2} - 21 r t + 90 t^{2}

Solution

a^{2} + 11 a b + 18 b^{2}

= (a + 2 b) (a + 9 b)

b^{2} - 2 b z - 24 z^{2}

= (b - 6 z) (b + 4 z)

x^{2} - 17 x y + 60 y^{2}

= (x - 12 y) (x - 5 y)

r^{2} - 21 r t + 90 t^{2}

= (r - 6 t) (r - 15 t)