Question

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Chứng minh:

(x + y) (x² - xy + y²) = (x + y)³ - 3xy (x + y)

 

Answer 1

Ta có :

\(VP=x^3+3x^2y+3xy^2+y^3-3x^2y-3xy^2\)

\(=x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)=VT\)

\(\RightarrowĐPCM\)

Answer 2

VT = x³ + y³ ( HĐT số 6 )

= x³ + 3x²y + 3xy² + y³ - 3x²y - 3xy²

= ( x³ + 3x²y + 3xy² + y³ ) - ( 3x²y + 3xy² )

= ( x + y )³ - 3xy( x + y ) = VP

=> đpcm

Answer 3

\(\left(x+y\right)\left(x^2-xy+y^2\right)=\left(x+y\right)^3-3xy\left(x+y\right)\)

\(VT=x^3+3x^2y+3xy^2+y^3-3x^2y-3xy^2=x^3+y^3\)

Mà \(x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)\)

Ta có đpcm 

Answer 4

\(\left(x+y\right)\left(x^2-xy+y^2\right)=\left(x+y\right)^3-3xy\left(x+y\right)\)

\(VT=x^3+3x^2y+3xy^2+y^3-3x^2y-3xy^2=x^3+y^3\)

Mà \(x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)\)

Ta có đpcm