Question

Phân tích đa thức thành nhân tử (Áp dụng phương pháp nhóm)

a) x² - x - y² - y

b) x² - 2xy - z² + y²

c) 5x - 5y + ax - ay

Giúp e với, e cảm ơn !

Answer 1

a) \(x^2-x-y^2+y\)

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

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

b) \(x^2-2xy-z^2+y^2\)

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

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

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

c) \(5x-5y+ax-ay\)

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

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

Answer 2

a) x² - x - y² - y

= (x^2 - y^2) - (x+y)

= (x+y) (x-y) - (x+y)

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

b) x² - 2xy - z² + y²

= (x^2 - 2xy + y^2 ) - z^2 

= (x-y)^ 2- z^2

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

c) 5x - 5y + ax - ay

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

= (5+a)(x-y)

Answer 3

a) x² - x - y² - y  =  (x² - y²) - (x+y) = (x-y)(x+y) - (x+y) = (x+y). ( x- y - 1)

b) x² - 2xy - z² + y²  = (x² - 2xy + y² ) - z² = (x-y)² - z² = (x-y+z) . (x-y-z)

c) 5x - 5y + ax - ay = 5.(x-y) + a(x-y) = (5+a) . ( x-y) 

Answer 4

x² - x - y² - y = x² - y² - x - y = (x - y)(x + y) - (x + y) = (x - y - 1)(x + y)

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

Câu b tớ chịu , sorry !

Answer 5

a) =( x²-y²) - x-y = (x-y)(x+y) - (x+y) = (x+y)(x-y-1)

b) = (x²-2xy+y²) - z² = (x-y)² -z² = (x-y-z)(x-y+z)

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