Algebra - Identities & Simplification

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1. If x+y+30, then find the value of x³ + y³- 9xy + 9  Option: (a) - 18 (b)-36 (c) 18 (d) 36

Solⁿ

Given: x + y + 3 = 0  ⇒  x + y = −3

Find: x³ + y³ - 9xy + 9

Use the identity: x³+y³ = (x+y)³-3xy(x+y)

Substitute x + y = −3

                                x³ + y³ = (−3)³−3xy(−3) = −27 + 9xy

Now put into the given expression:

                                x³ + y³ - 9xy + 9 = (−27 + 9xy) − 9xy + 9 = −18

Ans: (a) −18

Exam Tip: When you see x³+y^3,  x³ and x+y is given, always use

x³+y³ = (x + y)³-3xy(x + y