Question

Phân tích thành nhân tử

A) x^2 - x- y^2 - y

B) x^2 - 2xy + y^2 - z^2

C) 5x - 5y + ax - ay

Answer 1

a) \(x^2-x-y^2-y\)

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

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

\(=\left(x+y\right)\left(x-y-1\right)\)

b) \(x^2-2xy+y^2-z^2\)

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

\(=\left(x-y\right)^2-z^2\)

\(=\left(x-y-z\right)\left(x-y+z\right)\)

c) \(5x-5y+ax-ay\)

\(=\left(5x-5y\right)+\left(ax-ay\right)\)

\(=5\left(x-y\right)+a\left(x-y\right)\)

\(=\left(x-y\right)\left(5+a\right)\)

Answer 2

A) x² - x- y² - y

=(x²-y²)-(x+y)

=(x-y)(x+y)-(x+y)

=(x+y)(x-y-1)

B) x² - 2xy + y² - z²

= (x²-2xy+y²)-z²

=(x-y)²-z²

=(x-y+z)(x-y-z)

C) 5x - 5y + ax - ay

= (5x-5y)+(ax-ay)

=5(x-y)+a(x-y)

= (x-y)(5+a)