EDGE Math 8

Products of Two Binomials

The product of two binomials $a + b$ and $c + d$ can be found using the FOIL (which is an acronym for first, outside, inside, and last) method. By applying the distributive property twice, you will get

Example 1

Multiply each of the following:

a. $(5 p^{2} + 2 q) (- 3 p^{2} + 10 q)$

b. $(x y^{3} - 8 z) (2 x^{3} y + 3 w)$

Solution

Use the FOIL method. Then combine like terms.

(5 p^{2} + 2 q) (- 3 p^{2} + 10 q)

= (5 p^{2}) (- 3 p^{2}) + (5 p^{2}) (10 q)

+ (2 q) (- 3 p^{2}) + (2 q) (10 q)

= - 15 p^{4} + 50 p^{2} q - 6 p^{2} q + 20 q^{2}

= - 15 p^{4} + 44 p^{2} q + 20 q^{2}

(x y^{3} - 8 z) (2 x^{3} y + 3 w)

= (x y^{3}) (2 x^{3} y) + (x y^{3}) (3 w)

+ (- 8 z) (2 x^{3} y) + (- 8 z) (3 w)

= 2 x^{4} y^{4} + 3 w x y^{3} - 16 x^{3} y z - 24 w z