FOIL MATH PROBLEM

Question

 

FOIL: (3X+7)(3X-7)

Answer 1

(a + b)(a - b) = a² - b² (difference of squares)

(3x + 7)(3x - 7)

(3x)² - 7²

9x² - 49

Answer 2

Foil multiplying as follows

F: First: (3x)*(3x)

O: Outer: (3x)*(-7)

I: Inner:  (7)*(3x)

L: Last: (7)*(-7)

 

So if its all put together,

 

      F               O            I             L

(3x)*(3x)+(3x)*(-7)+(7)*(3x)+(7)*(-7)

9x²-21x+21x-49

9x²-49

 

The original problem is what you call a difference of squares, where (ax+b)(ax-b). When you FOIL and simplify, the middle terms (in our case -21x and 21x) cancel out. Therefore, you are left with a²x²-b² as a difference of squares.