Algebra I

Multiplying Polynomials (FOIL)

Lesson

To multiply two binomials (two-term polynomials), use the FOIL method:

Then add up all four products and combine any like terms.

Worked example 1

(x + 3)(x + 5)

FOIL:

Add and combine like terms:

x^2 + 5x + 3x + 15 = x^2 + 8x + 15

Worked example 2 — with subtraction

(x - 4)(x + 2)

The signs travel with each term:

x^2 + 2x - 4x - 8 = x^2 - 2x - 8

How to type your answer

Write terms in descending order of exponent (highest first). Use ^ for exponents. No spaces. Examples: x^2+8x+15, x^2-2x-8, 2x^2+7x-15.

Work through these. Stuck? Click Get a hint.

Quick problems to get going.

Problem 1

(x + 1)(x + 2)

Problem 2

(x + 2)(x + 4)

Problem 3

(x + 1)(x + 1)

Problem 4

(x + 3)(x + 2)

Standard problems matching the lesson.

Problem 5

(x + 3)(x + 5)

Problem 6

(x + 4)(x + 6)

Problem 7

(x - 4)(x + 2)

Problem 8

(x + 7)(x - 3)

Problem 9

(x - 2)(x - 5)

Problem 10

(x - 6)(x - 1)

Problem 11

(x + 5)(x - 5)

Problem 12

(x - 3)(x + 3)

Problem 13

(2x + 1)(x + 3)

Problem 14

(3x - 2)(x + 4)

Problem 15

(x + 4)^2

Problem 16

(x - 5)^2

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 17

(2x + 3)(2x - 3)

Problem 18

(3x + 2)(2x + 5)

Problem 19

(4x - 1)(x - 6)

Problem 20

(2x + 7)^2

Problem 21

(5x - 3)(2x + 4)

Problem 22

(x + 2)(x^2 + 3x + 1)