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\(a,6x^2-9x=3x\left(x-3\right)\)
\(b,x^3-2x^2-3x+6\)
\(=\left(x^3-2x^2\right)-\left(3x-6\right)\)
\(=x^2\left(x-2\right)-3\left(x-2\right)\)
\(=\left(x^2-3\right)\left(x-2\right)\)
\(e,2x\left(x-y\right)-3y\left(x-y\right)\)
\(=\left(2x-3y\right)\left(x-y\right)\)
a) 6x2 - 9x
= 3x (2x - 3)
b) x3 - 2x2 - 3x + 6
= x2(x - 2) - 3 (x - 2)
=(x - 2) (x2 - 3)
c) x2 - 4x + 4 - 9y2
= (x - 2)2 - 9y2
=(x - 2 - 3y)(x - 2 + 3y)
e) 2x(x - y) - 3y(x - y)
= (x - y)(2x - 3y)
xin lỗi mình học ngu nên không biết làm nhìu nha
\(a,2x^2y-xy^2\)
\(=xy.\left(2x-y\right)\)
\(b,x^4+4x^2-5\)
\(x^4+5x^2-x^2-5\)
\(=x^2.\left(x^2+5\right)-\left(x^2+5\right)=\left(x^2+1\right).\left(x^2+5\right)\)
1, x2+3xy+2y2= x2+xy+2xy+2y2=x(x+y)+2y(x+y)=(x+2y)(x+y)
2, x(x+2)(x+3)(x+5)+9=x(x+5)(x+2)(x+3)+9=(x2+5x)(x2+5x+6)+9
Đặt x2+5x=t, ta có
t(t+6)+9=t2+6t+9=(t+3)2=(x2+5x+3)2=(x2+8)2
3, x2+2xy+y2+2x+2y-15=(x+y)2+2(x+y)-15=(x+y)2+2(x+y)+1-16=(x+y+1)2-42
= (x+y+1-4)(x+y+1+4)=(x+y-3)(x+y+5)
4, 4x4y4+1=4x4y4+4x2y2+1-4x2y2=(2x2y2+1)2-(2xy)2=(2x2y2+1-2xy)(2x2y2+1+2xy)
a) x2 + 4x + 3 - y2 -2y
= x2 +4x + 4 - y2 -2y-1
= (x+2)2 - (y+1)2
= (x+2-y-1).(x+2+y+1)
= (x-y+1).(x+y+3)
b) 2a2 -5ab + 2b2
= 2a2 -4ab + 2b2 - ab
= 2.(a2 - 2ab+b2) - ab
= 2.(a-b)2 -ab
...
c) (x+y)2 - 2x - 2y + 1
= (x+y)2 - 1 - 2x -2y +2
= (x+y-1).(x+y+1) - 2.(x+y-1)
= (x+y-1)2
a)x(x2+2xy+y2-4)
=x[(x+y)2-22 ]
=x(x+y-2)(x+y+2)
b)x4+4=x4+4x2+4-4x2=(x2+2)2-4x2
=(x2+2-2x)(x2+2+2x)
\(x^3+2x^2y+xy^2-4x=x\)\(\left(x^2+2xy+y^2-4\right)\)
\(=x\left[\left(x+y\right)^2-4\right]\)
\(=x\left(x+y+2\right)\left(x+y-2\right)\)
\(x^4+4=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2\)
\(=\left(x^2+2+2x\right)\left(x^2+2-2x\right)\)
a) \(x^3-3x+1-3x^2=\left(x^3+1\right)-\left(3x^2+3x\right)=\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1-3x\right)=\left(x+1\right)\left(x^2-4x+1\right)\)
b) \(2x^2+4x+2-2y^2=2\left(x^2+2x+1-y^2\right)=2\left[\left(x+1\right)^2-y^2\right]=2\left(x+1+y\right)\left(x+1-y\right)\)