Question

( x + y ) mũ 3 - x mũ 3 - y mũ 3

x mũ 3 + 1 - x mũ 2 - x

oa oa , mik quên lun cách lm r , men nào giúp mik vs

Answer 1

Phân tích đa thức thành nhân tử à?

1) \(\left(x+y\right)^3-x^3-y^3\)

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

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

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

\(=3xy\left(x+y\right)\)

2) \(x^3+1-x^2-x\)

\(=\left(x+1\right)\left(x^2-x+1\right)-x\left(x+1\right)\)

\(=\left(x+1\right)\left[x^2-x+1-x\right]\)

\(=\left(x+1\right)\left(x^2-2x+1\right)\)

\(=\left(x+1\right)\left(x-1\right)^2\)

Answer 2

( x + y )³ - x³ - y³

= ( x + y )³ - ( x³ + y³ )

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

= ( x + y )[ ( x + y )² - ( x² - xy + y² ) ]

= ( x + y )( x² + 2xy + y² - x² + xy - y² )

= 3xy( x + y )

x³ + 1 - x² - x

= ( x³ + 1 ) - ( x² + x )

= ( x + 1 )( x² - x + 1 ) - x( x + 1 )

= ( x + 1 )( x² - x + 1 - x )

= ( x + 1 )( x² - 2x + 1 )

= ( x + 1 )( x - 1 )²

Answer 3

\(\left(x+y\right)^3-x^3-y^3\)

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

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

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

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

\(=3xy\left(x+y\right)\)