Question

Why ( a+b)^2 =a^2 +b^2+2ab

Answer 1

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$(a + b) {}^{2} = (a + b)(a + b) \\ = a {}^{2} + ab + ab + b {}^{2} \\ = a {}^{2} + b {}^{2} + 2ab$

Answer 2

(a+b)^2=(a+b)(a+b)

a^2+ab+ba+b^2

we know that algebraic product is associative

a^2+b^2+2ab