# Verify:(i) x3 + y3 = (x + y) (x2 + y2 – xy)(ii) x3 – y3 = (x – y) (x2 + y2 + xy)

Concept Used:

(x + y)3 = x3 + y3 + 3xy (x + y)

(x – y)3 = x3 – y3 – 3xy (x – y)

Explanation:

(i) We know that,

(x + y)3 = x3 + y3 + 3xy (x + y)

x3 + y3 = (x + y)3 – 3xy (x + y)

[Taking (x + y) common]
x3 + y3 = (x + y) [(x + y)2 – 3xy)

x3 + y3 = (x + y) [(x2 + y2 + 2xy) – 3xy]

[(x + y)2 = x2 + y2 + 2 x y]

x3 + y3 = (x + y) (x2 + y2 – xy)

(ii) We know that,

(x – y)3 = x3 – y3 – 3xy (x – y)

x3 – y3 = (x – y)3 + 3xy (x – y)
[Taking (x – y) common]

x3 – y3 = (x – y) [(x – y)2 + 3xy)

x3 – y3 = (x – y) [(x2 + y2 – 2xy) + 3xy]

[(x – y)2 = x2 + y2 – 2 x y]

= x3 – y3 = (x – y) (x2 + y2 + xy)

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