Question

prove that (a+b)2=a2+2ab+b2​

Answer 1

Answer:

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

          =(a+b)(a)+(a+b)(b)

         =a2+ab+ab+b2

          =a2+2ab+b2

hence proved

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Answer 2

Hello !

Here , we have to prove that (a+b)²= a²+2ab+b².

So let's start,

(a+b)²

→ (a+b)×(a+b)

→ (a+b)(a+b)

→ [a×(a+b)]+[b×(a+b)]

→ [(a×a)+(a×b)]+[(b×a)+(b×b)]

→ [(a²)+(ab)]+[(ba)+(b²)]

→ (a²)+(ab)+(ba)+(b²)

Since, a×b = b×a (communicative property) ba = ab.

→ (a²)+(ab)+(ab)+(b²)

→ a² + 2 × ab + b²

→ a²+2ab+b²

Hence proved✓