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Year 9 · Patterns & Algebra

Expand (ax + b)(cx + d)

Polynomials add and subtract by collecting like terms, and multiply by expanding every pair.

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How to do it

  1. Add: combine x² with x², x with x, numbers with numbers.
  2. Subtract: change every sign in the second bracket, then add.
  3. Multiply: each term times each term, then collect.

Worked example

(2x + 1)(x + 3)
2x² + 6x + x + 3
2x² + 7x + 3

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Subtracting a negative term adds it.

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