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Expanding Double Brackets Practice
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Expanding Double Brackets Practice
Expand each pair of brackets by multiplying every term in the first bracket by every term in the second. Collect like terms and take care with negative signs. Show your working.
Warm-up: collect the terms
Begin with positive terms, then spot the pattern in the final question.
1.Expand (x + 2)(x + 3).
2.Expand (a + 4)(a + 6).
3.A rectangle has side lengths (x + 3) cm and (x + 5) cm. Write and simplify an expression for its area.
Mixed signs and coefficients
Multiply carefully: a negative term changes the sign of its product.
4.Expand (x + 4)(x − 2).
5.Expand (x − 3)(x − 4).
6.Expand (2x + 1)(x + 3).
7.A student expands (x − 2)(x + 5) and writes x² + 3x − 10. Is the result correct? If not, identify the error and give the correct expansion.
Pattern spotters
Use structure to expand quickly and work backwards from a quadratic.
8.Expand (x + 7)(x − 7). What special pattern do you notice?
9.Choose the correct expansion of (x + 2)(x + 5).
- x² + 7x + 10
- x² + 10x + 7
- x² + 5x + 2
- x² + 2x + 5
10.The expansion of (x + a)(x + b) is x² + 8x + 15. Find the positive integers a and b. Explain how you know.
11.Create a pair of brackets of the form (x + m)(x + n) that expands to x² + 9x + 20. State your brackets and verify by expanding.
2 printable pages
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