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a) \(=\left(x-2y\right)\left(x^2+5x\right)\)
b) \(=\left(x-1\right)\left(x^2+2x+1\right)=\left(x-1\right)\left(x+1\right)^2\)
c) \(=\left(x^2+1-2x\right)\left(x^2+1+2x\right)\)
\(=\left(x^2-2x+1\right)\left(x^2+2x+1\right)\)
\(=\left(x-1\right)^2\left(x+1\right)^2\)
d) \(=3\left(x+3\right)-\left(x-3\right)\left(x+3\right)\)
\(=\left(x+3\right)\left(3-x+3\right)\)
\(=\left(x+3\right)\left(6-x\right)\)
e) \(=\left(x^2-\frac{1}{3}x\right)\left(x^2+\frac{1}{3}x\right)\)
f) \(=2x\left(x-y\right)-16\left(x-y\right)\)
\(=2\left(x-y\right)\left(x-8\right)\)
a) 4x2-8x=0
(2x)2-2.2.2x+4-4=0
(2x-2)2 =4
2x-2=2
2x =4
x=2
Nhớ k cho mk nha
a) \(x^3-x^2-5x+125\)
\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
b) \(5x^2-5xy-3x+3y\)
\(=5x\left(x-y\right)-3\left(x-y\right)\)
\(=\left(x-y\right)\left(5x-3\right)\)
c) \(x^2-2x-4y^2+1\)
\(=\left(x-1\right)^2-4y^2\)
\(=\left(x-2y-1\right)\left(x+2y-1\right)\)
Bài 1:
a) \(2x^3-x^2-2x+1\) (đã sửa đề)
\(=x^2\left(2x-1\right)-\left(2x-1\right)\)
\(=\left(x^2-1\right)\left(2x-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(2x-1\right)\)
b) \(4x^2-16x^2y^2+y^2+4xy\)
\(=\left(4x^2+4xy+y^2\right)-16x^2y^2\)
\(=\left(2x+y\right)^2-\left(4xy\right)^2\)
\(=\left(2x-4xy+y\right)\left(2x+4xy+y\right)\)
c) \(x^3-16x-15x\left(x-4\right)\)
\(=x^3-16x-15x^2+60x\)
\(=x^3-15x^2+44x\)
\(=x\left(x^2-15x+44\right)\)
\(=x\left(x-4\right)\left(x-11\right)\)
d) \(x\left(x-y\right)+y\left(x-y\right)^2-xy+x^2\)
\(=x\left(x-y\right)+y\left(x-y\right)^2+x\left(x-y\right)\)
\(=\left(x-y\right)\left[x+y\left(x-y\right)+x\right]\)
\(=\left(x-y\right)\left(2x+xy-y^2\right)\)
Bài 2:
a) \(x^4+1-2x^2\)
\(=\left(x^2\right)^2-2x^2+1\)
\(=\left(x^2-1\right)^2\)
\(=\left(x-1\right)^2\left(x+1\right)^2\)
b) \(x^2-y^2-3y+3x\)
\(=\left(x-y\right)\left(x+y\right)+3\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y+3\right)\)
c) \(y^2-4x^2+4x-1\) (đã sửa đề)
\(=y^2-\left(2x-1\right)^2\)
\(=\left(y-2x+1\right)\left(y+2x-1\right)\)
d) \(x^3\left(2+1\right)^2-\left(x+2\right)^2+1-x^3\)
\(=9x^3-x^2-4x-4+1-x^3\)
\(=8x^3-x^2-4x-3\)
\(=\left(8x^3-8x^2\right)+\left(7x^2-7x\right)+\left(3x-3\right)\)
\(=\left(x-1\right)\left(8x^2+7x+3\right)\)