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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:

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

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