Phân tích thành nhân tử :
a) y2 (x2 + y) - z2 -zy
b) 16x2 - ( x2 + 4)2
c) (x+y)3 + ( x-y)3
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Những câu hỏi liên quan
22 tháng 12 2022
a: \(=5x\left(xy^2+3x+6y^2\right)\)
b: \(=\left(x-2\right)\left(x+3\right)-\left(x-2\right)\left(x+2\right)=\left(x-2\right)\left(x+3-x-2\right)=\left(x-2\right)\)
c: \(=\left(x-3\right)\left(x-4\right)\)
d: \(=x\left(x^2-2xy+y^2-9\right)\)
=x(x-y-3)(x-y+3)
e: \(=\left(x+y\right)^2-25=\left(x+y+5\right)\left(x+y-5\right)\)
f: \(=\left(x-4\right)\left(x+3\right)\)
1 tháng 11 2023
a: \(x^2-9-x^2\left(x^2-9\right)\)
\(=\left(x^2-9\right)-x^2\left(x^2-9\right)\)
\(=\left(x^2-9\right)\left(1-x^2\right)\)
\(=\left(1-x\right)\left(1+x\right)\left(x-3\right)\left(x+3\right)\)
b: \(x^2\left(x-y\right)+y^2\left(y-x\right)\)
\(=x^2\left(x-y\right)-y^2\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2-y^2\right)\)
\(=\left(x-y\right)\left(x-y\right)\left(x+y\right)=\left(x-y\right)^2\cdot\left(x+y\right)\)
c: \(x^3+27+\left(x+3\right)\left(x-9\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)\)
\(=\left(x+3\right)\left(x^2-3x+9+x-9\right)\)
\(=\left(x+3\right)\left(x^2-2x\right)=x\left(x-2\right)\left(x+3\right)\)
d: \(x^2+5x+6\)
\(=x^2+2x+3x+6\)
\(=x\left(x+2\right)+3\left(x+2\right)=\left(x+2\right)\left(x+3\right)\)
e: \(3x^2-4x-4\)
\(=3x^2-6x+2x-4\)
\(=3x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(3x+2\right)\)
g: \(x^4+64y^4\)
\(=x^4+16x^2y^2+64y^4-16x^2y^2\)
\(=\left(x^2+8y^2\right)^2-\left(4xy\right)^2\)
\(=\left(x^2+8y^2-4xy\right)\left(x^2+8y^2+4xy\right)\)
1 tháng 11 2023
h: \(a^2+b^2+2a-2b-2ab\)
\(=a^2-2ab+b^2+2a-2b\)
\(=\left(a-b\right)^2+2\left(a-b\right)=\left(a-b\right)\left(a-b+2\right)\)
i: \(\left(x+1\right)^2-2\left(x+1\right)\left(y-3\right)+\left(y-3\right)^2\)
\(=\left(x+1-y+3\right)^2\)
\(=\left(x-y+4\right)^2\)
k: \(x^2\left(x+1\right)-2x\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-2x+1\right)\)
\(=\left(x+1\right)\left(x-1\right)^2\)
CM
13 tháng 10 2017
x 2 y + x y 2 + x 2 z + x z 2 + y 2 z + y z 2 + 3xyz.
= ( x 2 y + x 2 z + xyz) + (x y 2 + y 2 z + xyz) + (x z 2 + y z 2 + xyz)
= x(xy + xz + yz) + y(xy + yz + xz) + z(xz + yz + xy)
= (x + y + z)(xy + xz + yz).
NC
14 tháng 12 2020
\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)
\(=\left(x^2y+x^2z+xyz\right)+\left(xz^2+yz^2+xyz\right)+\left(xy^2+y^2z+xyz\right)\)
\(=x\left(xy+xz+yz\right)+z\left(xz+yz+xy\right)+y\left(xy+yz+xz\right)\)
\(=\left(x+y+z\right)\left(xy+yz+xz\right)\)
T
27 tháng 10 2023
a, \(8^3yz+12^2yz+6xyz+yz\)
\(=512yz+144yz+6xyz+yz\)
\(=yz\left(512+14+6x+1\right)\)
\(=yz\left(527+6x\right)\)
$---$
b, \(81x^4\left(z^2-y^2\right)-z^2+y^2\)
\(=81x^4\left(z^2-y^2\right)-\left(z^2-y^2\right)\)
\(=\left(z^2-y^2\right)\left(81x^4-1\right)\)
\(=\left(z-y\right)\left(z+y\right)\left[\left(9x^2\right)^2-1^2\right]\)
\(=\left(z-y\right)\left(z+y\right)\left(9x^2-1\right)\left(9x^2+1\right)\)
\(=\left(z-y\right)\left(z+y\right)\left[\left(3x\right)^2-1^2\right]\left(9x^2+1\right)\)
\(=\left(z-y\right)\left(z+y\right)\left(3x-1\right)\left(3x+1\right)\left(9x^2+1\right)\)
$---$
c, \(\dfrac{x^3}{8}-\dfrac{y^3}{27}+\dfrac{x}{2}-\dfrac{y}{3}\)
\(=\left[\left(\dfrac{x}{2}\right)^3-\left(\dfrac{y}{3}\right)^3\right]+\left(\dfrac{x}{2}-\dfrac{y}{3}\right)\)
\(=\left(\dfrac{x}{2}-\dfrac{y}{3}\right)\left(\dfrac{x^2}{4}+\dfrac{xy}{6}+\dfrac{y^2}{9}\right)+\left(\dfrac{x}{2}-\dfrac{y}{3}\right)\)
\(=\left(\dfrac{x}{2}-\dfrac{y}{3}\right)\left(\dfrac{x^2}{4}+\dfrac{xy}{6}+\dfrac{y^2}{9}+1\right)\)
$---$
d, \(x^6+x^4+x^2y^2+y^4-y^6\)
\(=\left(x^6-y^6\right)+\left(x^4+x^2y^2+y^4\right)\)
\(=\left[\left(x^2\right)^3-\left(y^2\right)^3\right]+\left(x^4+x^2y^2+y^4\right)\)
\(=\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)+\left(x^4+x^2y^2+y^4\right)\)
\(=\left(x^4+x^2y^2+y^4\right)\left(x^2-y^2+1\right)\)
$Toru$
CM
31 tháng 1 2017
a) (x - 1)(x - 2). b) 4(x - 2)(x - 7).
c) (x + 2)(2x +1). d) (x - l)(2x - 7).
e) (2x + 3y - 3)(2x - 3y +1). g) (x - 3)( x 3 + x 2 - x +1).
h) (x + y)(x + y-l)(x + y + l).
XO
19 tháng 6 2021
a) (x + y)2 - 2(x + y) + 1
= (x + y)2 - 2.1.(x + y) + 1
= (x + y - 1)2
b) x3 + 1 - x2 - x
= (x3 - x2) - (x - 1)
= x2(x - 1) - (x - 1)
= (x2 - 1)(x - 1) = (x - 1)(x + 1)(x - 1) = (x - 1)2(x + 1)
c) 27x3 - 0,001
= \(\left(3x\right)^3-\frac{1}{1000}=\left(3x\right)^3-\left(\frac{1}{10}\right)^3=\left(3x-\frac{1}{10}\right)\left(9x^2+\frac{3}{10}x+\frac{1}{100}\right)\)
d) 125x3 - 1 =(5x)3 - 1 = (5x - 1)(25x2 + 5x + 1)
e) (x2 + 4)2 - 16x2
= (x2 + 4)2 - (4x)2
= (x2 - 4x + 4)(x2 + 4x + 4)
= (x - 2)2(x + 2)2
= [(x - 2)(x + 2)]2
NC
19 tháng 6 2021
a.\(\left(x+y\right)^2-2\left(x+y\right)+1\)
\(=\left(x+y\right)^2-2.\left(x+y\right).1+1^2\)
\(=\left[\left(x+y\right)-1\right]^2\)
\(=\left(x+y-1\right)^2\)
b.\(x^3+1-x^2-x\)
\(=\left(x^3-x^2\right)+\left(1-x\right)\)
\(=x^2\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-1\right)\)
\(=\left(x-1\right)^2\left(x+1\right)\)
b) \(16x^2-\left(x^2+4\right)^2\)
\(=\left(4x-x^2-4\right)\left(4x+x^2+4\right)\)
\(=\left(-x^2+4x-4\right)\left(x+2\right)^2\)
\(=\left[-\left(x^2-4x+4\right)\right]\left(x+2\right)^2\)
\(=-\left(x-2\right)^2\left(x+2\right)^2\)
c) \(\left(x+y\right)^3+\left(x-y\right)^3\)
\(=\left(x+y+x-y\right)\left[\left(x+y\right)^2+2\left(x-y\right)\left(x+y\right)+\left(x-y\right)^2\right]\)
\(=2y\left[\left(x+y\right)\left(x+y+2x-2y\right)+\left(x-y\right)^2\right]\)
\(=2y\left[\left(x+y\right)\left(3x-y\right)+\left(x-y\right)^2\right]\)