Question

verify (i) x³+y³=(x+y) (x²–xy+y²) (ii) x³–y³=(x–y) (x²+xy+y²) using some non-zero positive integers and check by actual multiplication. Can you call these an identites​

Answer 1

Step-by-step explanation:

(i) x3+y3 = (x+y)(x2–xy+y2)

We know that, (x+y)3 = x3+y3+3xy(x+y)

⇒ x3+y3 = (x+y)3–3xy(x+y)

⇒ x3+y3 = (x+y)[(x+y)2–3xy]

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

⇒ x3+y3 = (x+y)(x2+y2–xy)

(ii) x3–y3 = (x–y)(x2+xy+y2)

We know that,(x–y)3 = x3–y3–3xy(x–y)

⇒ x3−y3 = (x–y)3+3xy(x–y)

⇒ x3−y3 = (x–y)[(x–y)2+3xy]

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

⇒ x3+y3 = (x–y)(x2+y2+xy)