Smart Age Lab

FOIL Method


Definition

The FOIL method is used to multiply two binomials.

FOIL stands for First, Outer, Inner, Last.

General form:
\( (a+b)(c+d) \)

FOIL Steps

F – First terms:
Multiply the first terms in each binomial.

O – Outer terms:
Multiply the outer terms.

I – Inner terms:
Multiply the inner terms.

L – Last terms:
Multiply the last terms.

Then combine like terms.

Worked Examples: Multiplying Binomials Using FOIL

1) \( (x+3)(x+5) \)

First: \(x \times x = x^2\)

Outer: \(x \times 5 = 5x\)

Inner: \(3 \times x = 3x\)

Last: \(3 \times 5 = 15\)

Write all terms together:
\(x^2+5x+3x+15\)

Combine like terms:
\(x^2+8x+15\)

2) \( (x+7)(x-3) \)

First: \(x \times x = x^2\)

Outer: \(x \times (-3) = -3x\)

Inner: \(7 \times x = 7x\)

Last: \(7 \times (-3) = -21\)

Write all terms together:
\(x^2-3x+7x-21\)

Combine like terms:
\(x^2+4x-21\)

3) \( (2x+3)(x+4) \)

First: \(2x \times x = 2x^2\)

Outer: \(2x \times 4 = 8x\)

Inner: \(3 \times x = 3x\)

Last: \(3 \times 4 = 12\)

Write all terms together:
\(2x^2+8x+3x+12\)

Combine like terms:
\(2x^2+11x+12\)

4) \( (x-4)(x-6) \)

First: \(x \times x = x^2\)

Outer: \(x \times (-6) = -6x\)

Inner: \((-4) \times x = -4x\)

Last: \((-4) \times (-6) = 24\)

Write all terms together:
\(x^2-6x-4x+24\)

Combine like terms:
\(x^2-10x+24\)

Practice Worksheet: Multiplying Binomials Using FOIL

  1. \( (x+2)(x+6)= \)
  2. \( (x+5)(x+3)= \)
  3. \( (x+4)(x-1)= \)
  4. \( (x+7)(x+8)= \)
  5. \( (x+9)(x+2)= \)
  6. \( (2x+3)(x+5)= \)
  7. \( (3x-1)(x-4)= \)
  8. \( (x+6)(x-2)= \)
  9. \( (2x+5)(x+3)= \)
  10. \( (x-10)(x+1)= \)
  11. \( (3x+2)(2x+5)= \)
  12. \( (4x-3)(x+2)= \)
  13. \( (2x-7)(3x+1)= \)
  14. \( (5x+2)(2x-3)= \)
  15. \( (3x-4)(2x-5)= \)