Algebra I

Multiplying Polynomials (FOIL)

Lesson

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

First — multiply the first terms
Outer — multiply the outer terms
Inner — multiply the inner terms
Last — multiply the last terms

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

Worked example 1

(x + 3)(x + 5)

FOIL:

F: $x \cdot x = x^2$
O: $x \cdot 5 = 5x$
I: $3 \cdot x = 3x$
L: $3 \cdot 5 = 15$

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:

F: $x \cdot x = x^2$
O: $x \cdot 2 = 2x$
I: $(-4) \cdot x = -4x$
L: $(-4) \cdot 2 = -8$

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.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

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)

Practice

Standard problems matching the lesson.

Problem 5

A rectangle has dimensions (x + 3) by (x + 5). Area as a polynomial?

Problem 6

A rectangle has dimensions (x + 4) by (x + 6). Area as a polynomial?

Problem 7

A rectangle has dimensions (x - 4) by (x + 2). Area as a polynomial?

Problem 8

A rectangle has dimensions (x + 7) by (x - 3). Area as a polynomial?

Problem 9

A rectangle has dimensions (x - 2) by (x - 5). Area as a polynomial?

Problem 10

A rectangle has dimensions (x - 6) by (x - 1). Area as a polynomial?

Problem 11

A rectangle has dimensions (x + 5) by (x - 5). Area as a polynomial?

Problem 12

A rectangle has dimensions (x - 3) by (x + 3). Area as a polynomial?

Problem 13

A rectangle has dimensions (2x + 1) by (x + 3). Area as a polynomial?

Problem 14

A rectangle has dimensions (3x - 2) by (x + 4). Area as a polynomial?

Problem 15

A square has side (x + 4). Area as a polynomial?

Problem 16

A square has side (x - 5). Area as a polynomial?

Challenge

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

Problem 17

A rectangle has dimensions (2x + 3) by (2x - 3). Area as a polynomial?

Problem 18

A rectangle has dimensions (3x + 2) by (2x + 5). Area as a polynomial?

Problem 19

A rectangle has dimensions (4x - 1) by (x - 6). Area as a polynomial?

Problem 20

A square has side (2x + 7). Area as a polynomial?

Problem 21

A rectangle has dimensions (5x - 3) by (2x + 4). Area as a polynomial?

Problem 22

A box has base side (x + 2) and a quadratic face area x^2 + 3x + 1. Total layered area as a polynomial?

Practice

Standard problems matching the lesson.

Problem 23

A rectangle has dimensions (x + 3) and (x + 5) meters. Find its area as a polynomial.

Problem 24

A square has side (x + 4) inches. Find its area as a polynomial.

Challenge

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

Problem 25

A patio is (2x + 3) wide and (2x - 3) long. Find its area as a polynomial.

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