Question

phân tích đa thức thành nhân tử :

1, x^2 - y^2 - x - y

2, x^4 - 5x^2 +4

3, 25 - x^2 + 2xy - y^2

thanks các pạn nhìu

Answer 1

1) x²-y²-x-y=(x²-y²)-(x+y)

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

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

2)x⁴-5x²+4

=x⁴-4x²-x²+4

=(x⁴-x²)-(4x²-4)

=x²(x²-1)-4(x²-1)

=(x²-1)(x²-4)

=(x-1)(x+1)(x-2)(x+2)

3)25-x²+2xy-y²

=25-(x²-2xy+y²)

=25-(x-y)²

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

Answer 2

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

2, x⁴-5x²+4=x⁴-x²-4x²+4=(x⁴-x²)-(4x²-4)=x²(x²-1)-4(x²-1)=(x²-1)(x²-4)

3, 25-x²+2xy-y²=5²-(x²-2xy+y²)=5²-(x-y)²=(5-x+y)(5+x-y)

Answer 3

_{1, \(x^2-y^2-x-y=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)}

_{=\(\left(x+y\right)\left(x-y-1\right)\)}

2, \(x^4-5x^2+4=x^4-4x^2-x^2+4\)

\(=x^2\left(x^2-4\right)-\left(x^2-4\right)\)

\(=\left(x^2-4\right)\left(x^2-1\right)\)

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

3, \(25-x^2+2xy-y^2=5^2-\left(x^2-2xy+y^2\right)\)

\(=5^2-\left(x-y\right)^2\)

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