Algebra
Expressions
Expanding expressions
19 practice questions
2 video lessons
Theory + worked examples
Theory
Expanding multiplies out a product using the distributive property. For two binomials, use FOIL:
\[(a+b)(c+d)=ac+ad+bc+bd,\]
which stands for First, Outer, Inner, Last.
Combine like terms after multiplying.
An area model expands \((x+3)(x+2)\).
FOIL for two binomials.
Expanding two binomials:
\[(a+b)(c+d)=ac+ad+bc+bd\]
Every term of one factor multiplies every term of the other.
How to expand
- Multiply each term of the first factor by each of the second.
- Track the signs.
- Combine like terms.
- Write in descending order.
Example 1 — Distribute a factor
Expand \(2(3x+5)\).
Solution
Distribute the \(2\).
| \(2(3x+5)\) | \(=\) | \(6x+10\) |
Example 2 — Two binomials (FOIL)
Expand \((x+3)(x+2)\).
Solution
Multiply each pair, then combine.
| \(x^2+2x+3x+6\) | ||
| \(=\) | \(x^2+5x+6\) |
Example 3 — A difference
Expand \((x-4)(x+1)\).
Solution
FOIL with signs.
| \(x^2+x-4x-4\) | ||
| \(=\) | \(x^2-3x-4\) |
Example 4 — Distribute a binomial
Expand \(x(2x-3)\).
Solution
Multiply \(x\) by each term.
| \(x(2x-3)\) | \(=\) | \(2x^2-3x\) |
Common pitfalls
Multiply every pair — don't miss the middle terms.
Watch the signs when a term is negative.
\((x+3)^2=x^2+6x+9\), not \(x^2+9\).
Frequently asked questions
What does expanding mean?
Multiplying out a product to remove parentheses.
What is FOIL?
First, Outer, Inner, Last — a way to multiply two binomials.
Expand \((x+2)(x+3)\).
\(x^2+5x+6\).
Is \((x+3)^2=x^2+9\)?
No — it is \(x^2+6x+9\).
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