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\(Bài1:\\ a,\left(4x-1\right)\left(2x^2-x-1\right)=4x\left(2x^2-x-1\right)-\left(2x^2-x-1\right)=8x^3-4x^2-4x-2x^2+x+1=8x^3-6x^2-3x+1\\ b,\left(4x^3+8x^2-2x\right):2x\\ =2x\left(2x^2+4x-1\right):2x\\ =2x^2+4x-1\)
\(Bài2:\\ a,2x^3-8x^2+8x=2x\left(x^2-4x+4\right)=2x\left(x-2\right)^2\\ b,2xy+2x+yz+z=2x\left(y+1\right)+z\left(y+1\right)=\left(y+1\right)\left(2x+z\right)\\ c,x^2+2x+1-y^2=\left(x+1\right)^2-y^2=\left(x-y+1\right)\left(x+y+1\right)\)
Bài 1:
\(a,2x^2y\left(2x^2y^2-xy^2\right)\\ =2x^2x^2y^2y-2x^2x.y^2.y=2x^4y^3-2x^3y^3\\ b,\left(x-1\right)\left(2x+3\right)\\ =x.2x+x.3-1.2x-1.3=2x^2+3x-2x-3\\ =2x^2+x-3\\ c,\left(20x^3y^4+10x^2y^3-5xy\right):5xy\\ =20x^3y^4:5xy+10x^2y^3:5xy-5xy:5xy\\ =\left(20:5\right).\left(x^3:x\right).\left(y^4:y\right)+\left(10:5\right).\left(x^2:x\right).\left(y^3:y\right)-\left(5:5\right).\left(x:x\right).\left(y:y\right)\\ =4x^2y^3+2xy^2-1\\ d,\left(y-3x\right)^2-\left(y^2-6xy\right)\\ =\left[y^2-2.y.3x+\left(3x\right)^2\right]-\left(y^2-6xy\right)\\ =y^2-6xy+9x^2-y^2+6xy =9x^2\)
Bài 2:
\(a,4xy+4xz=4x\left(y+z\right)\\ b,x^2-y^2+9-6x\\ =\left(x^2-6x+9\right)-y^2\\ =\left(x-3\right)^2-y^2\\ =\left(x-3-y\right)\left(x-3+y\right)\)
Bài 3:
\(a,\dfrac{3xy}{y+z}+\dfrac{3xz}{y+z}\\=\dfrac{3xy+3xz}{y+z}\\ =\dfrac{3x\left(y+z\right)}{\left(y+z\right)}=3x\left(Với:y\ne-z\right)\\ b,\dfrac{x}{x+2}-\dfrac{x}{x-2}\\ =\dfrac{x\left(x-2\right)-x\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}\\ =\dfrac{x^2-2x-x^2-2x}{\left(x+2\right)\left(x-2\right)}=0\)
\(a,=2x\left(x+3\right)\\ b,=x^3\left(x+3\right)+\left(x+3\right)=\left(x^3+1\right)\left(x+3\right)\\ =\left(x+1\right)\left(x+3\right)\left(x^2-x+1\right)\\ c,=64-\left(x-y\right)^2=\left(8-x+y\right)\left(8+x-y\right)\\ A=x^2+6x+5+x^3-8-x^2-x+2\\ A=x^3+5x-1\)
a) 2x2+6x=2x(x+3)
b) x4+3x3+x+3=(x4+x)+(3x3+3)=x(x3+1)+3(x3+1)=(x+3)(x3+1)
c) 64-x2-y2+2xy=-(x2-2xy+y2)+82=8-(x+y)2=(8+x+y)(8-x-y)
A= (x+5)(x+1)+(x-2)(x2+2xx+4)-(x2+x-2)
A= x2+6x+5+x3-8-x2-x+2
A= x3+(x2-x2)+(6x-x)+(5-8+2)
A= x3+5x-1
Bài 1:
b: \(=\left(x-2y\right)\left(x+2y\right)+4\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y+4\right)\)
c: \(=\left(x+y-3\right)\left(x+y+3\right)\)
Bài 1:
a: \(3xy^2-12x=3x\left(y^2-4\right)=3x\left(y-2\right)\left(y+2\right)\)
b: \(x^2-4y^2+4x+8y\)
\(=\left(x-2y\right)\left(x+2y\right)+4\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y+4\right)\)
Bài 1:
a: Ta có: \(\left(6x+3\right)-\left(2x-5\right)\left(2x+1\right)\)
\(=\left(2x+1\right)\left(3-2x+5\right)\)
\(=\left(2x+1\right)\left(8-2x\right)\)
\(=2\left(4-x\right)\left(2x+1\right)\)
b) Ta có: \(\left(3x-2\right)\left(4x-3\right)-\left(2-3x\right)\left(x-1\right)-2\left(3x-2\right)\left(x+1\right)\)
\(=\left(3x-2\right)\left(4x-3\right)+\left(3x-2\right)\left(x-1\right)-\left(3x-2\right)\left(2x+2\right)\)
\(=\left(3x-2\right)\left(4x-3+x-1-2x-2\right)\)
\(=\left(3x-2\right)\left(3x-6\right)\)
\(=3\left(3x-2\right)\left(x-2\right)\)
Bài 2:
a: Ta có: \(\left(a-b\right)\left(a+2b\right)-\left(b-a\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b\right)+\left(a-b\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b+2a-b-a-3b\right)\)
\(=\left(a-b\right)\left(2a-4b\right)\)
\(=2\left(a-b\right)\left(a-2b\right)\)
f: Ta có: \(x^2-6xy+9y^2+4x-12y\)
\(=\left(x-3y\right)^2+4\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x-3y+4\right)\)