M8 Expanding and factorising mind map

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M8 Expanding and factorising mind map

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Distribute: Every inside term; outside minus changes every sign
Two brackets: Every term × every term; collect middle terms

Common factors

Reverse: 12x²+8x = 4x(3x+2); expand to check
First step: Higher: 2x²−18 = 2(x−3)(x+3)

Quadratics

Sum / product: x²+7x+12 = (x+3)(x+4); check signs
Squares / solve: a²−b² = (a−b)(a+b); solving needs equation = 0

Further products

Non-monic: Higher: 6x²+7x+2 = (3x+2)(2x+1); check middle term
Three brackets: Higher: Expand two first, simplify, then multiply third

Connections

Expand → Common factors: Factorising reverses distribution
Expand → Quadratics: Expanded coefficients check quadratic factors