The word FOIL is a memory device for the words First, Outside, Inside, Last, which helps keep track of the multiplication when both sets of parentheses have two terms each.
Practice questions
- Simplify the expression (x + 7)(x – 2).
- Simplify the expression 6x – (x – 2)(x – 4) + 7x2.
Answers and explanations
- The answer is x2 + 5x – 14.
Begin by FOILing the parentheses. Start by multiplying the two first terms:
Multiply the two outside terms:
Multiply the two inside terms:
Finally, multiply the two last terms:
Add these four products together and simplify by combining like terms:
- The answer is 6x2 + 12x – 8.
Begin by FOILing the parentheses: Multiply the first, outside, inside, and last terms:
Add these four products together and put the result inside one set of parentheses, replacing the two sets of parentheses that were originally there:
6x – (x – 2)(x – 4) + 7x2 = 6x – (x2 – 4x – 2x + 8) + 7x2
The remaining set of parentheses is preceded by a minus sign, so change the sign of every term in there to its opposite and drop the parentheses:
= 6x – x2 + 4x + 2x – 8 + 7x2
Now simplify the expression by combining like terms and reordering your solution:
