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HG
2
KV
16 tháng 7 2023
(x + 2y)² - (x - y)²
= (x + 2y - x + y)(x + 2y + x - y)
= 3y(2x + y)
H9
HT.Phong (9A5)
CTVHS
16 tháng 7 2023
\(\left(x+2y\right)^2-\left(x-y\right)^2\)
\(=\left[\left(x+2y\right)-\left(x-y\right)\right]\left[\left(x+2y\right)+\left(x-y\right)\right]\)
\(=\left(x+2y-x+y\right)\left(x+2y+x-y\right)\)
\(=3y\left(2x+y\right)\)
28 tháng 10 2021
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:
\(a,=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y^2\right]=5\left(x-y+1\right)\left(x+y+1\right)\\ b,=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-4y^2\right]\\ =3x\left(x-2y-1\right)\left(x+2y-1\right)\\ c,=ab\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2\\ =\left(a+b\right)\left(a^2b-ab^2+a+b\right)\\ d,=2x\left(x^2-y^2-4x+4\right)=2x\left[\left(x-2\right)^2-y^2\right]\\ =2x\left(x-y-2\right)\left(x+y-2\right)\)
15 tháng 9 2018
\(\left(x^2-5\right)^2+144\)
\(=x^4-10x^2+25+144\)
\(=x^4-10x^2+169\)
\(=x^4+26x^2+169-36x^2\)
\(=\left(x^2+13\right)^2-\left(6x\right)^2\)
\(=\left(x^2-6x+13\right)\left(x^2+6x+13\right)\)
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, \(x^6+x^4+x^2y^2+y^4-y^6\)
\(=\left(x^6-y^6\right)+\left(x^4+x^2y^2+y^4\right)\)
\(=\left[\left(x^2\right)^3-\left(y^2\right)^3\right]+\left(x^4+x^2y^2+y^4\right)\)
\(=\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)+\left(x^4+x^2y^2+y^4\right)\)
\(=\left(x^4+x^2y^2+y^4\right)\left(x^2-y^2+1\right)\)
$Toru$
DT
2
3 tháng 4 2017
\(x^4+2002x^2+2001x+2002\)
\(=x^4+x^2+1+2001x^2+2001x+2001\)
\(=\left(x^4+2x^2+1\right)-x^2+2001\left(x^2+x+1\right)\)
\(=\left(x^2+1-x\right)\left(x^2+1+x\right)+2001\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2+1-x+2001\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+2002\right)\)
3 tháng 4 2017
\(x^4+2007x^2-2006x+2007\)
\(=x^4+2x^2+1-x^2+2006\left(x^2-x+1\right)\)
\(=\left(x^2+1\right)^2-x^2+2006\left(x^2-x+1\right)\)
\(=\left(x^2+1+x\right)\left(x^2+1-x\right)+2006\left(x^2-x+1\right)\)
\(=\left(x^2-x+1\right)\left(x^2+x+1+2006\right)\)
\(=\left(x^2-x+1\right)\left(x^2+x+2007\right)\)
27 tháng 11 2016
Cái đề này hợp lí hơn
a(b-c)2+b(c-a)2+c(a-b)2-a3-b3-c3+3abc
6 tháng 12 2021
\(=m^2-\left(n-2\right)^2=\left(m-n+2\right)\left(m+n-2\right)\)
81x4+4
=(9x2)2+22
=(9x2)2+36x2+22-36x2
=(9x2+2)2-(6x)2
=(9x2+2-6x)(9x2+2+6x)