How do you expand and simplify double brackets like (x + 3)(x − 5)?
Short answer
Multiply every term in the first bracket by every term in the second, then collect like terms. For (x + 3)(x − 5): x × x = x², x × (−5) = −5x, 3 × x = 3x, 3 × (−5) = −15, which simplifies to x² − 2x − 15.
Step by step
- Multiply the first term of the first bracket by each term in the second bracket.
- Multiply the second term of the first bracket by each term in the second bracket.
- Write all four results in a line, keeping each sign with its term.
- Collect the like terms, usually the two x terms in the middle.
Worked example
Expand (2x − 1)(x + 4)
- 2x × x = 2x²
- 2x × 4 = 8x
- −1 × x = −x
- −1 × 4 = −4
- Answer: 2x² + 7x − 4
Common mistakes
- Only multiplying the first terms and the last terms, giving x² − 15 and missing the middle.
- Dropping the sign of a negative term when multiplying.
- Writing (x + 3)² as x² + 9. It is (x + 3)(x + 3) = x² + 6x + 9.
Useful for:GCSEBECEBEPCCheckpoint
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