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a: \(3x^3-75x\)
\(=3x\left(x^2-25\right)\)
\(=3x\left(x-5\right)\left(x+5\right)\)
b: \(x^4y^2-12x^3y^2+48x^2y^2-64xy^2\)
\(=xy^2\left(x^3-12x^2+48x-64\right)\)
\(=xy^2\cdot\left(x-4\right)^3\)
a) \(x^4-4x^2-4x-1=\left(x^4-1\right)-4x\left(x+1\right)=\left(x^2+1\right)\left(x-1\right)\left(x+1\right)-4x\left(x+1\right)=\left(x+1\right)\left[\left(x^2+1\right)\left(x-1\right)-4x\right]=\left(x+1\right)\left(x^3-x^2+x-1-4x\right)=\left(x+1\right)\left(x^3-x^2-3x-1\right)\)
b) \(10x^4y^2-10x^3y^2-10x^2y^2+10xy^2=10xy^2\left(x^3-x^2-x+1\right)=10xy^2\left(x-1\right)^2\left(x+1\right)\)
a: \(x^4-4x^2-4x-1\)
\(=\left(x^4-1\right)-4x\left(x+1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)-4x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3+x-x^2-1-4x\right)\)
\(=\left(x+1\right)\left(x^3-x^2-3x-1\right)\)
b: \(10x^4y^2-10x^3y^2-10x^2y^2+10xy^2\)
\(=10xy^2\left(x^3-x^2-x+1\right)\)
\(=10xy^2\cdot\left[\left(x+1\right)\left(x^2-x+1\right)-x\left(x+1\right)\right]\)
\(=10xy^2\cdot\left(x+1\right)\left(x-1\right)^2\)
Bài 2:
1) \(x^2-4x+4=\left(x-2\right)^2\)
2) \(x^2-9=x^2-3^2=\left(x-3\right)\left(x+3\right)\)
3) \(1-8x^3=\left(1-2x\right)\left(1+2x+4x^2\right)\)
4) \(\left(x-y\right)^2-9x^2=\left(x-y\right)^2-\left(3x\right)^2=\left(x-y-3x\right)\left(x-y+3x\right)=\left(-2x-y\right)\left(4x-y\right)\)
5) \(\dfrac{1}{25}x^2-64y^2=\left(\dfrac{1}{5}x-8y\right)\left(\dfrac{1}{5}x+8y\right)\)
6) \(8x^3-\dfrac{1}{8}=\left(2x-\dfrac{1}{2}\right)\left(4x^2+x+\dfrac{1}{4}\right)\)
a) x4 + 2x3 + x2 = x2.(x2 + 2x + 1) = x2(x + 1)2
b) x3 - x + 3x2y + 3xy2 + y3 - y = x3 + 3x2y + 3xy2 + y3 - x - y = (x + y)3 - (x + y) = (x + y)[(x + y)2 - 1] = (x + y - 1)(x + y)(x + y + 1)
c) 5x2 - 10xy + 5y2 - 20z2 = 5.(x2 - 2xy + y2 - 4z2) = 5[(x - y)2 - (2z)2] = 5(x - y - 2z)(x - y + 2z)
\(a,x^4+2x^3+x^2=x^2\left(x^2+2x+1\right)=x^2\left(x+1\right)^2\)
\(b,x^3-x+3x^2y+3xy^2+y^3-y=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
\(c,5x^2-10xy+5y^2-20z^2=5\left(x^2-2xy+y^2-4z^2\right)=5\left[\left(x-y\right)^2-4z^2\right]\)
\(=5\left[\left(x-y+2z\right)\left(x-y-2z\right)\right]\)
\(3x^3+3x^2-36x\)
\(=3x\left(x^2+x-12\right)\)
\(=3x\left(x+4\right)\cdot\left(x-3\right)\)
\(x^3-x^2-x+1\)
\(=x^2\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-1\right)\)
Bài 1:
\(1,Sửa:x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\\ 2,=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\\ 3,=2y\left(y^2+4y+4\right)=2y\left(y+2\right)^2\\ 4,=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)
Bài 2:
\(1,=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\\ 2,=2y\left(4x^2-9\right)=2y\left(2x-3\right)\left(2x+3\right)\\ 3,=3\left(x^3-1\right)=3\left(x-1\right)\left(x^2+x+1\right)\)
Bài 3:
\(a,=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y^2\right]=5\left(x-y+1\right)\left(x+y+1\right)\\ b,=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-4y^2\right]\\ =3x\left(x-2y-1\right)\left(x+2y-1\right)\\ c,=ab\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2\\ =\left(a+b\right)\left(a^2b-ab^2+a+b\right)\\ d,=2x\left(x^2-y^2-4x+4\right)=2x\left[\left(x-2\right)^2-y^2\right]\\ =2x\left(x-y-2\right)\left(x+y-2\right)\)
a) \(5x^2y-20xy+20y=5y\left(x^2-4x+4\right)=5y\left(x-2\right)^2\)
b) \(3x^3+6x^2+3x=3x\left(x^2+2x+1\right)=3x\left(x+1\right)^2\)
c) \(3x^2y-12y=3y\left(x^2-4\right)=3y\left(x-2\right)\left(x+2\right)\)
d) \(7x^3-28x^2+28x=7x\left(x^2-4x+4\right)=7x\left(x-2\right)^2\)
a: \(5x^2y-20xy+20y\)
\(=4y\left(x^2-4x+4\right)\)
\(=4x\left(x-2\right)^2\)
b: \(3x^3+6x^2+3x\)
\(=3x\left(x^2+2x+1\right)\)
\(=3x\left(x+1\right)^2\)
c: \(3x^2y-12y\)
\(=3y\left(x^2-4\right)\)
\(=3y\left(x-2\right)\left(x+2\right)\)
d: \(7x^3-28x^2+28x\)
\(=7x\left(x^2-4x+4\right)\)
\(=7x\left(x-2\right)^2\)