Foiling Quadratic Functions

(X+A)(X+B) is the multiplication of two factors in a quadratic equation.  We also call it distribution.  A very easy way to solve these equation is with a term called Foiling.  Lets break it down.

First + Outside + Inside + Last

Example:

Expand (X+5)(X+3)

First (X)(X)=X² + Outside (X)(3)=3X +  Inside (5)(X)=5X + Last (5)(3)=15=X² + 8X + 15

Ah ha.  Now you know what foil means.

Lets try expanding (X-4)(X+3)

First (X)(X)=X² + Outside (X)(3)=3X +  Inside (-4)(X)=-4X + Last (-4)(3)=-12=X² -X -12

Something a little harder

Expand (-3X+7)(2X-4)

First (-3X)(2X)=-6X² + Outside (-3X)(-4)=-12X +  Inside (7)(2X)=14X + Last (7)(-24)=-28=

=-6X² +2X -28

Whohoo! Now try a few yourself:

1) (X+5)(X+2)

2) (X-3)(X+5)
3) (X+9)(X+1)

4) (3X+2)(X-7)
5) (6x-4)(3X-2)

Answers (1) x²+7x +10 (2) x²+2x-15 (3) x²+10x+9 (4) 3x²-19x-14 (5) 18x²+8