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Toolkit 10

Difference of squares

a2−b2=(a−b)(a+b)a^2-b^2=(a-b)(a+b)

Proof

Using the distributive law,

(a−b)(a+b)=a2+ab−ab−b2=a2−b2.□\begin{aligned} (a-b)(a+b) &= a^2 + ab - ab - b^2 \\ &= a^2 - b^2. \quad\square \end{aligned}
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