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1) x(x - y) + x - y
= x.(x - y) + (x - y)
= (x - y).(x + 1)
2) Câu b sai đề nên mk sửa lại nha
2x3 + x2 - 8x - 4
= (2x3 + x2) - (8x + 4)
= x2.(2x + 1) - 4.(2x + 1)
= (2x + 1).(x2 - 4)
= (2x + 1).(x - 2).(x + 2)
3) 2x2 - 8xy - 5x + 20y
= (2x2 - 5x) - (8xy - 20y)
= x.(2x - 5) - 4y.(2x - 5)
= (2x - 5).(x - 4y)
1) ( x+1) ( x-y)
2) 2x3 + x2 - 8x - 4= 2x3 - 4x2 + 5x2 - 10x + 2x - 4 = 2x2 ( x-2) + 5x( x -2) + 2(x -2)
=( 2x2 + 5x + 2)( x-2)
=( 2x2 + 4x + x + 2)( x-2)
=[ 2x( x+2) + ( x-2)]( x-2)
= ( 2x +1)( x+2)( x-2)
3) 2x2 - 8xy - 5x + 20y
= 2x ( x - 4y) - 5( x-4y)= ( 2x-5)(x-4y)
phân tích các đa thức sau thành nhân tử :
a ) 15x + 20y
b ) x2 - y2 -x +y
c ) x3 - 2x2 + x
d ) 64 - x6
a) = 5(3x+4y)
b) = (x2-y2) -(x-y)
= (x-y)(x+y)-(x-y)
=(x-y)(x+y+1)
c) = x(x2+x+1)
= x(x+1)2
d) = (23)2-(x3)2
= (23-x3)(23+x3)
a, = 5(3x+4y)
b,=(x-y)(x+y)-(x-y)
=(x-y)(x+y+1)
c,=x(x2-2x+1)
=x(x-1)2
d,=(23-x3)(23+x3)
\(x^2+y^2-x^2y^2+xy-x-y\)
\(=x^2-x^2y^2+y^2-y+xy-x\)
\(=x^2\left(1-y^2\right)+y\left(y-1\right)+x\left(y-1\right)\)
\(=x^2\left(1-y\right)\left(y+1\right)+y\left(y-1\right)+x\left(y-1\right)\)
\(=\left(y-1\right)\left[-x^2\left(y+1\right)+y-x\right]\)
\(=\left(y-1\right)\left[-x^2y-x^2+y-x\right]\)
b,(xy+4)2-4(x+y)2
=(xy+4)2-(2(x+y))2
=(xy+4)2-(2x+2y)^2
=(xy+4-2x-2y)(xy+4+2x+2y)
\(x^2+xy-20y^2\)
\(=x^2+2.x.\frac{1}{2}y+\frac{1}{4}y^2-20y^2-\frac{1}{4}y^2\)
\(=\left(x+\frac{1}{2}y\right)^2-\frac{79}{4}\)
\(=\left(x+\frac{1}{2}y-\frac{\sqrt{79}}{2}\right)\left(x+\frac{1}{2}y+\frac{\sqrt{79}}{2}\right)\)