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Multiplying Two Binomials

MATH LESSON

BINOMIAL × BINOMIAL

Learn the FOIL Method — the fastest way to multiply two binomials!

What is FOIL?

FOIL stands for the order of multiplying terms:

First — Multiply the first terms of each binomial
Outer — Multiply the outer terms (leftmost × rightmost)
Inner — Multiply the inner terms (rightmost × leftmost)
Last — Multiply the last terms of each binomial
How to Apply FOIL

After getting the 4 products, combine like terms (terms with the same variable and exponent).

(x + 3)(x + 2)
F: x · x = x²
O: x · 2 = 2x
I: 3 · x = 3x
L: 3 · 2 = 6
Combine: x² + 5x + 6
Watch Out for Signs!

When a binomial has a negative sign, be careful — it affects the sign of every product that uses that term.

(2x − 1)(x + 4)
F: 2x · x = 2x²
O: 2x · 4 = 8x
I: (−1) · x = −x
L: (−1) · 4 = −4
Combine 8x − x = 7x: 2x² + 7x − 4
More Examples
Example 1: (x + 5)(x − 2)
F: x²   O: −2x   I: +5x   L: −10
→ x² + 3x − 10 = x² + 3x − 10
Example 2: (3x − 2)(x + 1)
F: 3x²   O: +3x   I: −2x   L: −2
→ 3x² + x − 2 = 3x² + x − 2
Example 3: (x − 4)(x − 3)
F: x²   O: −3x   I: −4x   L: +12
→ x² − 7x + 12 = x² − 7x + 12
Example 4: (2x + 3)(2x + 3)
F: 4x²   O: +6x   I: +6x   L: +9
→ 4x² + 12x + 9 = 4x² + 12x + 9

Remember: FOIL gives you 4 terms → always check if you can combine like terms (the O and I terms)!

LEARNING CHECK

Let's see what you learned!

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MATH QUIZ

Quiz Time!

10 questions about Binomial × Binomial. You got this!

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Made for students who want to master Binomial × Binomial

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