(a + b) give the answer by expansion
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13
(a +b)2
= (a + b)(a + b)
= a(a + b) + b(a+ b)
= a2 + ab + ab + b2
= a2 + 2ab + b2.
(a - b)2
= (a - b)(a - b)
= a(a - b) - b(a - b)
= a2 - ab - ab + b2
= a2 - 2ab + b2.
Therefore, (a + b)2 + (a - b)2
= a2 + 2ab + b2 + a2 - 2ab + b2
= 2(a2 + b2), and
(a + b)2 - (a - b)2
= a2 + 2ab + b2 - {a2 - 2ab + b2}
= a2 + 2ab + b2 - a2 + 2ab - b2
= 4ab.
Answered by
4
Answer:
Expansion of (a ± b)2
(a +b)2
= (a + b)(a + b)
= a(a + b) + b(a+ b)
= a2 + ab + ab + b2
= a2 + 2ab + b2.
(a - b)2
= (a - b)(a - b)
= a(a - b) - b(a - b)
= a2 - ab - ab + b2
= a2 - 2ab + b2.
Therefore, (a + b)2 + (a - b)2
= a2 + 2ab + b2 + a2 - 2ab + b2
= 2(a2 + b2), and
(a + b)2 - (a - b)2
= a2 + 2ab + b2 - {a2 - 2ab + b2}
= a2 + 2ab + b2 - a2 + 2ab - b2
= 4ab.
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