Special products and factors
(x
+ y)² = x² + 2xy + y²
(x − y)² = x² − 2xy + y²
(x + y)3
= x3 + 3x² y + 3xy² + y3
(x − y)3 = x3
− 3x² y + 3xy² − y3
(x + y)4 = x4 + 4x3
y + 6x² y² + 4xy3 + y4
(x − y)4 = x4
− 4x3 y + 6x² y² − 4xy3 + y4
(x + y)5
= x5 + 5x4 y + 10x3 y² + 10x² y3 +
5xy4 + y5
(x − y)5 = x5 − 5x4
y + 10x3 y² − 10x² y3 + 5xy4 − y5
(x + y)6 = x6 + 6x5 y + 15x4 y²
+ 20x3 y3 + 15x² y4 + 6xy5 + y6
(x − y)6 = x6 − 6x5 y + 15x4 y²
− 20x3 y3 + 15x² y4 − 6xy5 + y6
x²
− y² = (x − y)(x + y)
x3 − y3 = (x − y)(x² + xy +
y² )
x3 + y3 = (x + y)(x² − xy + y² )
x4
− y4 = (x − y)(x + y)(x² + y² )
x5 − y5
= (x − y)(x4 + x3 y + x² y² + xy3 + y4
)
x5 + y5 = (x + y)(x4 − x3 y
+ x² y² − xy3 + y4 )
x6 − y6
= (x − y)(x + y)(x² + xy + y² )(x² − xy + y² )
x4
+ x² y² + y4 = (x² + xy + y² )(x² − xy + y² )
x4 +
4y4 = (x² + 2xy + 2y² )(x² − 2xy + 2y² )