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Expanding Double Brackets

Learn how to expand double brackets, using the formula (a + b)(c + d) = ac + ad + bc + bd, and simplify the result. Let’s get started! 🚀

Expanding Double Brackets - introduction visual

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Flashcards

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Visual explanation of the distributive law showing b(c + d) equals bc + bd using coloured rectanglesExpanding double brackets showing the binomial product formula (a+b)(c+d)=ac+ad+bc+bd step-by-step. Example (2x - 1)(3x + 2) for expanding double brackets, fully simplified to 6x² + x - 2.Example (-3x + 2)(5 - y) for expanding double brackets, fully simplified to -15x + 3xy + 10 - 2y.

🛎️ The Distributive Law

  • The distributive law means multiplying a term by everything inside the brackets.
  • For example, b(c+d)=bc+bdb(c+d)=bc+bd.

🛎️ Binomial Products: Formula

  • A binomial product means multiplying two brackets together.
  • For (a+b)(c+d)(a+b)(c+d), multiply every pair to get ac+ad+bc+bdac+ad+bc+bd.

🛎️ Expanding Two Brackets: Example

  • Always include the signs when multiplying terms.
  • For example, (2x−1)(3x+2)=2x⋅3x+2x⋅2−1⋅3x−1⋅2(2x-1)(3x+2)=2x\cdot3x+2x\cdot2-1\cdot3x-1\cdot2.

🛎️ Expanding with Negatives

  • Rewrite subtraction as adding a negative before expanding.
  • For example, (−3x+2)(5−y)=(−3x)⋅5+(−3x)⋅(−y)+2⋅5+2⋅(−y)(-3x+2)(5-y)=(-3x)\cdot5+(-3x)\cdot(-y)+2\cdot5+2\cdot(-y).

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Interactive Activity

Expanding double brackets: distribute and collect like terms

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