Question

Use foil to explain how to find the product of (a+b)(a-b). Then describe a shortcut that you could use to get this product without using foil.

Answer 1

Using the FOIL method -
Firsts: a×a= a^2
Outers: a×-b= -ab
Inners: b×a= ab
Lasts: b×-b= -b^2

Combine -
a^2-ab+ab-b^2
= a^2-b^2

This particular pair of binomial brackets with a + and a - in them can be expanded with the difference of two squares:
(a+b)(a-b) = a^2-b^2
This works for binomial brackets with a + and a - in each of them, and where the two terms in each bracket are the sameFor example:
(x+5)(x-5)= x^2-25
So remember,
Difference
Of
Two
Squares,
Abbreviated as D.O.T.S

Answer 2

FOIL stands for Front Outter Inner Last

F- multiply the first two terms axa= a^2
O- multiply the two terms on the outside a x -b= -ab
I- multiply the two inner (middle) terms - b x a= ab
L- multiply the last variable in each term= b^2


A shortcut without using FOIL is called the difference of squares and can be rewrote as (a^2-b^2)