Question

(a + b)² = a² + 2ab + b²​

Answer 1

Step-by-step explanation:

(a+b)²

= (a+b)×(a+b)

= (a+b)(a+b)

= [a×(a+b)]+[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 (commutative property), ba = ab.

= (a²)+(ab)+(ab)+(b²)

= (a²)+(2×ab)+(b²)

= (a²)+(2ab)+(b²)

Without Algebra, proof that (a+b)² is not equal to a²+b²

Let a = 5, and b = 4.

In (a+b)²,

= (5+4)²

= (9)²

= 9×9

= 81,

Whereas in a² + b²

= 5² + 4²

= 25 + 16

= 41.

Order of operations makes all the difference, if you add 5 and 4 before squaring the term, the answer is 81, whereas if you square 5 and then square 4 and add the two results, the final answer is different. And the Parentheses are placed in (a+b)² is just so as to signify that the two terms, “a” and “b” are to be added before squaring them. (a+b)² will always be greater than a² + b².

Answer 2

Property of algebra -

${(a+b) × (a+b)}$

${a(a+b) + b(a+b)}$

${a^2+ab+ab+b^2}$

${a^2+2ab+b^2}$