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Question -

Verify:

(i) x3+y=(x+y)(x2–xy+y2)

(ii) x3–y=(x–y)(x2+xy+y2)



Answer -

(i) x3+y=(x+y)(x2–xy+y2)

We know that, (x+y)3 = x3+y3+3xy(x+y)

x3+y=(x+y)3–3xy(x+y)

x3+y=(x+y)[(x+y)2–3xy]

Taking (x+y) common x3+y= (x+y)[(x2+y2+2xy)–3xy]

x3+y=(x+y)(x2+y2–xy)


(ii) x3–y=(x–y)(x2+xy+y2

We know that,(x–y)3 = x3–y3–3xy(x–y)

x3−y=(x–y)3+3xy(x–y)

x3−y=(x–y)[(x–y)2+3xy]

Taking (x+y) common x3−y= (x–y)[(x2+y2–2xy)+3xy]

x3+y=(x–y)(x2+y2+xy)

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