Phân tích đa thức sau bằng phương pháp nhóm hạng tử
1) x ( a - b ) + a - b ; 2) x - y - a( x - y ) ; 3) a( x + y ) - x - y ; 4) x( a - b ) - a + b ; 5) x\(^2\) + xy - 2x - 2y
6) 10ax - 5ay + 2x - y ; 7) 2a\(^{^2}\) x - 5by - 5a\(^2\) y + 2bx ; 8) 2ax\(^2\)- bx\(^2\) - 2ax + bx + 4a - 2b ; 9) 2ax - bx + 3cx - 2a + b - 3c
10) ax - bx - 2cx - 2a + 2b + 4c
1, x(a-b)+a-b 2, x-y-a(x-y) 3, a(x+y)-x-y 4, x(a-b)-a+b 5, x2+xy-2x-2y 6, 10ax-5ay+2x-y
= x(a-b)+(a-b) =(x-y)-a(x-y) =a(x+y)-(x+y) =x(a-b)-(a-b) =(x2+xy)-(2x+2y) =(10ax+2x)-(5ay+y)
=(a-b)(x+1) =(x-y)(1-a) =(x+y)(a-1) =(a-b)(x-1) =x(x+y)-2(x+y) =2x(5a+1)-y(5a+1)
=(x+y)(x-2) =(5a+1)(2x-y)
7, 2a2x-5by-5a2y+2bx 8, 2ax2-bx2-2ax+bx+4a-2b 9, 2ax-bx+3cx-2a+b-3c 10, ax-bx-2cx-2a+2b+4c
=(2a2x+2bx)-(5by+5a2y) =(2ax2-bx2)-(2ax-bx)+(4a-2b) =(2ax-2a)-(bx-b)+(3cx-3c) =(ax-2a)-(bx-2b)-(2cx-4c)
=2x(a2+b)-5y(b+a2) =x2(2a-b)-x(2a-b)+2(2a-b) =2a(x-1)-b(x-1)+3c(x-1) =a(x-2)-b(x-2)-2c(x-2)
=(a2+b)(2x-5y) =(2a-b)(x2-x+2) =(x-1)(2a-b+3c) =(x-2)(a-b-2c)
\(1)x\left(a-b\right)+a-b=x\left(a-b\right)+\left(a-b\right)=\left(x+1\right)\left(a-b\right)\)
\(2)x-y-a\left(x-y\right)=\left(x-y\right)-a\left(x-y\right)=\left(1-a\right)\left(x-y\right)\)
\(3)a\left(x+y\right)-x-y=a\left(x+y\right)-\left(x+y\right)=\left(a-1\right)\left(x+y\right)\)
\(4)x\left(a-b\right)-a+b=x\left(a-b\right)-\left(a-b\right)=\left(x-1\right)\left(a-b\right)\)
\(5)x^2+xy-2x-2y=\left(x^2+xy\right)-\left(2x+2y\right)=x\left(x+y\right)-2\left(x+y\right)=\left(x-2\right)\left(x+y\right)\)
\(6)10ax-5ay+2x-y=\left(10ax-5ay\right)+\left(2x-y\right)=5a\left(2x-y\right)+\left(2x-y\right)=\left(5a+1\right)\left(2x-y\right)\)
\(7)2a^2x-5by-5a^2y+2bx=\left(2a^2x+2bx\right)-\left(5by+5a^2y\right)=2x\left(a^2+b\right)-5y\left(b+a^2\right)=\left(2x-5y\right)\left(a^2+b\right)\)
\(8)2ax^2-bx^2-2ax+bx+4a-2b=\left(2ax^2-2ax+4a\right)-\left(bx^2-4x+2b\right)=2a\left(x^2-x+2\right)-b\left(x^2-x+2\right)=\left(2a-b\right)\left(x^2-x+2\right)\)
\(9)2ax-bx+3cx-2a+b-3c=\left(2ax-2a\right)-\left(bx-b\right)+\left(3cx-3c\right)=2a\left(x-1\right)-b\left(x-1\right)+3c\left(x-1\right)=\left(2a-b+3x\right)\left(x-1\right)\)
\(10)ax-bx-2cx-2a+2b+4c=\left(ax-2a\right)-\left(bx-2b\right)-\left(2cx-4c\right)=a\left(x-2\right)-b\left(x-2\right)-2c\left(x-2\right)=\left(a-b-2x\right)\left(x-2\right)\)
