prove that (x + y)^3= x^3 + y^3 + 3 xy ( x + y ) natural numbers
Answers
To prove :
(x + y)³ = x³ + y³ + 3 xy ( x + y )
Step-by-step explanation:
=> (x + y)³ = (x + y) (x + y) (x + y)
= [ (x + y) (x + y) ] (x + y)
= [ x(x + y) + y(x + y) ] (x + y)
= [ x(x) + x(y) + y(x) + y(y) ] (x + y)
= [ x² + xy + xy + y² ] (x + y)
= [ x² + 2xy + y² ] (x + y)
= x² (x + y) + 2xy(x + y) + y²(x + y)
= x²(x) + x²(y) + 2xy(x) + 2xy(y) + y²(x) + y²(y)
= x³ + x²y + 2x²y + 2xy² + xy² + y³
= x³ + y³ + x²y + 2x²y + 2xy² + xy²
= x³ + y³ + 3x²y + 3xy²
= x³ + y³ + 3xy(x) + 3xy(y)
= x³ + y³ + 3xy(x + y)
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Some of the standard algebraic identities are :
- (a + b)² = a² + 2ab + b²
- (a – b)² = a² – 2ab + b²
- a² – b² = (a + b)(a – b)
- (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
- (a + b)³ = a³ + b³ + 3ab (a + b)
- (a – b)³ = a³ – b³ – 3ab (a – b)
Step-by-step explanation:
Please kindly refer the attachment................
