Expand double brackets
Objective. Expand two binomials systematically.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Expanding double brackets means multiplying two linear binomials together to produce a quadratic expression. Each term in the first bracket must multiply every term in the second bracket, often remembered using the FOIL order: First, Outer, Inner, Last. For example, (x + 3)(x + 2) expands to x² + 2x + 3x + 6, which simplifies to x² + 5x + 6 after combining the like terms 2x and 3x. Signs must be tracked carefully, since a negative term in either bracket changes the sign of the resulting product. The final step is always to collect like terms into a single simplified quadratic expression.
Worked example
Expand and simplify the double brackets (x − 4)(x + 7).
- 1Multiply the first terms: x × x = x².
- 2Multiply outer and inner terms: x × 7 = 7x and −4 × x = −4x.
- 3Multiply the last terms: −4 × 7 = −28.
- 4Combine: x² + 7x − 4x − 28 = x² + 3x − 28.
Answer: x² + 3x − 28
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils frequently forget to multiply both 'outer' and 'inner' pairs, only multiplying the first and last terms, giving an incomplete expansion like x² + 6 instead of x² + 5x + 6. Multiply every term in the first bracket by every term in the second.
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