high School⏱ 3 min

Binomial Square

Why (a+b)² = a²+2ab+b²

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a²a·ba·bb²a = 3b = 2ab
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Values

In general

(a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2

For your values

(3+2)2=32+2⋅3⋅2+22=9+12+4=25(3+2)^2 = 3^2 + 2 \cdot 3 \cdot 2 + 2^2 = 9 + 12 + 4 = 25

Explanation

A square with side (a+b) splits into 4 areas: two squares (a² and b²) and two rectangles (each a·b). Total: a² + 2ab + b².