3.5 Binomial products

Introduction

The distributive law is: $a(b+c)=ab+ac$ . Essentially, the a is “in-multiplied” into the bracket.

For example, $(4y-8x)(y+9x)=4y(y+9x)-8x(y+9x)=4y^2+36xy-8xy-72x^2=4y^2+28xy-72x^2$

To find binomial products, the steps are, using the above as an example:

Multiply first terms (4y, y), meaning $4y*y=4y^2$
Multiply outer terms (4y, 9y), meaning $4y*9x=36xy$
Multiply inner terms (-8x, y), meaning $-8x*y=-8xy$
Multiply last terms (-8x, 9x), meaning $-8x*9x=-72x^2$
Simplify, putting together the above $4y^2+36xy-8xy-72x^2=4y^2+28xy-72x^2$