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a)27x3+27x2+9x+1+x+1/3
=(3x+1)3+1/3(3x+1)
=(3x+1)[(3x+1)2+1/3]
=(3x+1)(9x2+6x+4/3)
b)8xy3-5xyz-24y2+15z
=(8xy3-24y2)-(5xyz-15z)
=8y2(xy-3)-5z(xy-3)
=(xy-3)(8y2-5z)
c)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)
d)a6-a4-2a3+2a2
=a4(a-1)(a+1)-2a2(a-1)
=(a-1)(a5+a4-2a2)
=(a-1)(a5-a4+2a4-2a2)
=(a-1)[a4(a-1)+2a2(a-1)(a+1)]
=(a-1)(a-1)(a4+2a3+2a2)
=(a-1)2(a4+2a3+2a2)
\(x^4+x^3+x+1\)
\(=x^3\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3+1\right)\)
\(=\left(x+1\right)^2\left(x^2-x+1\right)\)
a,\(x^2y^2+y^3+zx^2+yz=\left(x^2y^2+y^3\right)+\left(zx^2+yz\right)\)
\(=y^2\left(x^2+y\right)+z\left(x^2+y\right)\)
\(=\left(y^2+z\right)\left(x^2+y\right)\)
b,\(x^4+2x^3-4x-4=x^4+2x^3+x^2-x^2-4x-4\)
\(=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)
\(=\left(x^2+x\right)^2-\left(x+2\right)^2\)
\(=\left(x^2+x-x-2\right)\left(x^2+x+x+2\right)\)
\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)
c,\(x^3+2x^2y-x-2y=\left(x^3+2x^2y\right)-\left(x+2y\right)\)
\(=x^2\left(x+2y\right)-\left(x+2y\right)\)
\(=\left(x^2-1\right)\left(x+2y\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x+2y\right)\)
\(x^4+4x^2-5\)
\(=\left(x^4+4x^2+4\right)-9\)
\(=\left(x^2+2\right)^2-9\)
\(=\left(x^2+2+3\right)\left(x^2+2-3\right)\)
\(=\left(x^2+5\right)\left(x^2-1\right)\)
a.
\(x^4-x^3-x+1=x^3\times\left(x-1\right)-\left(x-1\right)=\left(x-1\right)\left(x^3-1\right)=\left(x-1\right)\left(x-1\right)\left(x^2+x+1\right)=\left(x-1\right)^2\left(x^2+x+1\right)\)
b.
\(8xy^3-5xyz-24y^2+15z=8y^2\times\left(xy-3\right)-5z\left(xy-3\right)=\left(xy-3\right)\left(8y^2-5z\right)\)
c.
\(x^2-y^2+2x+1=\left(x+1\right)^2-y^2=\left(x-y+1\right)\left(x+y+1\right)\)
d.
\(x^2+2xz-y^2+2ty+z^2-t^2=\left(x+z\right)^2-\left(y-t\right)^2=\left(x+z+y-t\right)\left(x+z-y+t\right)\)
e.
\(2x^2-y^2+xy=2x^2+2xy-y^2-xy=2x\times\left(x+y\right)-y\times\left(x+y\right)=\left(2x-y\right)\left(x+y\right)\)
f.
\(y^2-y-12=y^2-3y+4y-12=y\times\left(y-3\right)+4\times\left(y-3\right)=\left(y-3\right)\left(y+4\right)\)
\(x^4-x^3-x+1\)
\(=x^3\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3-1\right)\)
\(=\left(x-1\right)\left(x-1\right)\left(x^2+x+1\right)\)
\(=\left(x-1\right)^2\left(x^2+x+1\right)\)
\(a)\) \(x^2-2x-4y^2-4y\)
\(=\)\(\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)\)
\(=\)\(\left(x-1\right)^2-\left(2y+1\right)^2\)
\(=\)\(\left(x-1-2y-1\right)\left(x-1+2y+1\right)\)
\(=\)\(\left(x-2y-2\right)\left(x+2y\right)\)
\(=\)\(2\left(x-y\right)\left(x+2y\right)\)
Chúc bạn học tốt ~
a) Ta có x2 - 2x - 4y2 - 4y
= x2 - 2x + 1 - 4y2 - 4y - 1
= (x - 1)2 - (4y2 + 4y + 1)
= (x - 1)2 - (2y + 1)2
= (x - 1 - 2y - 1)(x - 1 + 2y + 1)
= (x - 2y - 1)(x + 2y)
a)
\(=x^2\left(2x+3\right)+\left(2x+3\right)\)
\(=\left(x^2+1\right)\left(2x+3\right)\)
b)
\(=a\left(a-b\right)+a-b\)
\(=\left(a+1\right)\left(a-b\right)\)
c)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left(x+1-y\right)\left(x+1+y\right)\)
d)
\(=x^3\left(x-2\right)+10x\left(x-2\right)\)
\(=x\left(x^2+10\right)\left(x-2\right)\)
e)
\(=x\left(x^2+2x+1\right)\)
\(=x\left(x+1\right)^2\)
f)
\(=y\left(x+y\right)-\left(x+y\right)\)
\(=\left(y-1\right)\left(x+y\right)\)
a,2x3+3x2+2x+3
=(2x3+2x)+(3x2+3)
=2x(x2+1)+3(x2+1)
=(x2+1)(2x+3)
b,a2-ab+a-b
=(a2-ab)+(a-b)
=a(a-b)+(a-b)
=(a-b)(a+1)
c,2x2+4x+2-2y2
=2(x2+2x+1-y2)
=2[(x2+2x+1)-y2 ]
=2[(x+1)2-y2 ]
=2(x+1-y)(x+1+y)
d,x4-2x3+10x2-20x
=(x4-2x3)+(10x2-20x)
=x3(x-2)+10x(x-2)
=(x-2)(x3+10x)
=(x-2)[x(x2+10)]
e,x3+2x2+x
=x(x2+2x+1)
=x(x+1)2
f,xy+y2-x-y
=(xy+y2)-(x-y)
=y(x+y)-(x+y)
=(x+y)(y-1)
A) 1/2 x(x^2-4)+4(x+2)
=1/2x(x-2)(x+2)+4(x+2)
=(x+2)(1/2x^2-x+4)
b) 21(x-y)^2-7(x-y)^3
= (x-y)^2(21-7x+7y)
=(x-y)^2.7(3-x+y)
c) 1/8x^3-3/4x^2+3/2x-1
=(1/2x)^3-3.(1/2x)^2.1+3.1/2x.1^2-1
=(1/2x-1)^3
a) = x3(x-1)-(x-1)
=(x-1)(x3-1)
=(x-1)(x-1)(x2+x+1)