Question

Chứng minh:

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

Answer 1

(x + y)³ = x³ + 3x²y + 3xy² + y³

=> x³ + y³

= (x + y)³ - 3x²y - 3xy²

= (x + y)³ - 3xy(x + y)

= (x + y)[(x + y)² - 3xy]

= (x + y)(x² + 2xy + y² - 3xy)

= (x + y)(x² - xy + y²)

=> đpcm

Answer 2

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

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

\(=x^3+y^3=VT\)

\(\RightarrowĐPCM\)