Question

Simplify: (x + y)³ - x³ - y³​

Answer 1

SOLUTION

TO SIMPLIFY

$\sf {(x + y)}^{3} - {x}^{3} - {y}^{3}$

FORMULA TO BE IMPLEMENTED

We are aware of the formula that

$\sf {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)$

EVALUATION

Here the given expression is

$\sf {(x + y)}^{3} - {x}^{3} - {y}^{3}$

We simplify it as below

$\sf {(x + y)}^{3} - {x}^{3} - {y}^{3}$

$\sf = {x}^{3} + {y}^{3} + 3xy(x + y) - {x}^{3} - {y}^{3}$

$\sf = 3xy(x + y)$

FINAL ANSWER

$\sf {(x + y)}^{3} - {x}^{3} - {y}^{3} = 3xy(x + y)$

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