Question

verify that (x+y)^3= x^3+y^3+3xy(x+y)​

Answer 1

Question:

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

Answer:

We will expand LHS.

(x+y)³ = (x + y) (x + y)²

[using algebraic identity {a+b}²= a²+b²+2ab ]

= (x + y) (x² + y² + 2xy)

= x³ + xy² + 2x²y + x²y + y³ + 2xy²

= x³ + y³ + 3x²y + 3xy²

= x³ + y³ + 3xy (x+y)

LHS = RHS

Hence verified.

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