a² +2ab and -3ab - d²
Answers
+2ab and -3ab - d²(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.
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