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Expanding Brackets

Year 8 📊 Algebra Expand single and double brackets, simplify expressions.

Expanding a bracket means multiplying every term inside by the term outside.

⚡ Distributive Law

$$a(b + c) = ab + ac$$

Example: Expand $3(2x - 5) = 6x - 15$

Example: Expand $-2(x + 4) = -2x - 8$

💡 Watch the signs carefully when the outside term is negative — a negative times a positive gives a negative.

Multiply each term in the first bracket by each term in the second.

⚡ FOIL: First, Outer, Inner, Last

$$(x+a)(x+b) = x^2 + bx + ax + ab = x^2 + (a+b)x + ab$$

Example: $(x+3)(x-2) = x^2 - 2x + 3x - 6 = x^2 + x - 6$

Two expansions appear so often that they deserve their own names.

⚡ Perfect Square

$$(x+a)^2 = x^2 + 2ax + a^2$$

⚡ Difference of Two Squares

$$(x+a)(x-a) = x^2 - a^2$$

Example: $(x+5)^2 = x^2 + 10x + 25$

Example: $(x+7)(x-7) = x^2 - 49$

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🎬 Interactive Demonstration — Expanding Brackets

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🧮 📦 Bracket Expander

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