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a) x^4 - x^3 - x + 1
= x^3 ( x - 1 ) - ( x- 1 )
= ( x^3 - 1 )(x - 1)
= ( x- 1 )^2 (x^2 + x + 1 )
a)x4-x3-x+1
=x3(x-1)-(x-1)
=(x-1)(x3-1)
=(x-1)(x-1)(x2+x+1)
=(x-1)2(x2+x+1)
b)5x2-4x+20xy-8y
(sai đề)
a,\(xy+3x-7y-21\)
\(=x\left(y+3\right)-7\left(y+3\right)\)
\(=\left(y+3\right)\left(x-7\right)\)
\(b,2xy-15-6x+5y\)
\(=\left(2xy-6x\right)+\left(-15+5y\right)\)
\(=2x\left(y-3\right)-5\left(3-y\right)\)
\(=2x\left(y-3\right)+5\left(y-3\right)\)
\(=\left(y-3\right)\left(2x+5\right)\)
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) \(4x^3y-12x^2y^3-8x^4y^3\)
\(=4x^2y\left(x-3y^2-2x^2y^2\right)\)
b) \(2x^2+4x+2-2y^2\)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left[\left(x+1\right)^2-y^2\right]\)
\(=2\left(x-y+1\right)\left(x+y+1\right)\)
c) \(x^3-2x^2+x-xy^2\)
\(=x\left(x^2-2x+1-y^2\right)\)
\(=x\left[\left(x-1\right)^2-y^2\right]\)
\(=x\left(x-y-1\right)\left(x+y-1\right)\)
d) \(x\left(x-2y\right)+3\left(2y-x\right)\)
\(=x\left(x-2y\right)-3\left(x-2y\right)\)
\(=\left(x-3\right)\left(x-2y\right)\)
e) \(x^2+4\)
\(=\left(x^4+4x^2+4\right)-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2\)
\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
f) \(5x^2-7x-6\)
\(=\left(5x^2-10x\right)+\left(3x-6\right)\)
\(=5x\left(x-2\right)+3\left(x-2\right)\)
\(=\left(5x+3\right)\left(x-2\right)\)
\(a,2x^2-4xy+2y^2-8t^2\)
\(=2\left[\left(x^2-2xy+y^2\right)-4t^2\right]\)
\(=2\left[\left(x-y\right)^2-\left(2t^2\right)\right]-\)
\(=2\left(x-y+2t\right)\left(x-y-2t\right)\)
\(b,x^3+x+3x^2y+2xy^2+y^3+y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)+\left(x+y\right)\)
\(=\left(x+y\right)^3+\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2+1\right]\)
\(=\left(x+y\right)\left(x^2+2xy+y^2+1\right)\)
\(c,x^4-7x^2=x^2\left(x^2-7\right)\)
\(=x^2\left(x+\sqrt{7}\right)\left(x-\sqrt{7}\right)\)
Sửa đề:\(d,5x-5y-x^2+2xy-y^2\)
\(=5\left(x-y\right)-\left(x-y\right)^2\)
\(=\left(x-y\right)\left(5-x+y\right)\)
\(e,x^4+4x^3+4x^2-x^2y^2\)
\(=\left(x^4+4x^3+4x^2\right)-x^2y^2\)
\(=\left(x^2+2x\right)^2-\left(xy\right)^2\)
\(=\left(x^2+2x+xy\right)\left(x^2+2x-xy\right)\)
\(g,x^2-y^2-2y-1\)
\(=x^2-\left(y+1\right)^2\)
\(=\left(x+y+1\right)\left(x-y-1\right)\)
a) \(2x^2-4xy+2y^2-8t^2=2\left(x^2-2xy+y^2-4t^2\right)\)
\(=2\left(\left(x-y\right)^2-\left(2t\right)^2\right)=2\left(x-y-2t\right)\left(x-y+2t\right)\)
b) \(x^3+x+3x^2y+3xy^2+y^3+y=\left(x^3+3x^2y+3xy^2+y^3\right)+\left(x+y\right)\)
\(=\left(x+y\right)^3+\left(x+y\right)=\left(x+y\right)^2\left(x+y\right)+\left(x+y\right)\)
\(=\left(x^2+2xy+y^2\right)\left(x+y\right)+\left(x+y\right)=\left(x^2+2xy+y^2+1\right)\left(x+y\right)\)
c) \(x^4-7x^2=\left(x^2\right)^2-\left(\sqrt{7}x\right)^2=\left(x^2-\sqrt{7}x\right)\left(x^2+\sqrt{7}x\right)\)
d) câu này hình như đề sai thì phải
e) \(x^4+4x^3+4x^2-x^2y^2=x^2\left(x^2+4x+4-y^2\right)\)
\(=x^2\left(\left(x+2\right)^2-y^2\right)=x^2\left(x+2-y\right)\left(x+2+y\right)\)
g) \(x^2-y^2-2y-1=x^2-\left(y^2+2y+1\right)=x^2-\left(y+1\right)^2\)
\(=\left(x-y-1\right)\left(x+y+1\right)\)