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Question

Which of the following equations are correct?

(i) (a+b+c)2=a2+b2+c2+2(ab+bc+ca)
(ii) (a+b)3=a3+b3+3ab(ab)
(iii) (ab)3=a3b33ab(a+b)
(iv) a2b2=(a+b)(ab)


A
(iv) and (iii)
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B
(i) and (iv)
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C
(iv) only
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D
(ii), (iii) and (iv)
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Solution

The correct option is B (i) and (iv)
Use identity
(a+b+c)2=a2+b2+c2+2(ab+bc+ca)
(a+b)3=a3+b3+3ab(a+b)
(ab)3=a3b33ab(ab)
a2b2=(a+b)(ab)

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