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HT
21 tháng 7 2017
a) \(12x^2y-18xy^2-30y^2=6y\left(2x^2-3xy-5y\right)\)
b) \(5\left(x-y\right)-y\left(x-y\right)=\left(5-y\right)\left(x-y\right)\)
c) \(y\left(x-z\right)+7\left(z-x\right)=y\left(x-z\right)+7\left[-\left(x-z\right)\right]\)
\(=y\left(x-z\right)-7\left(x-z\right)\)
\(\left(y-7\right)\left(x-z\right)\)
d) \(36-12x+x^2=\left(6-x\right)^2\)
e) \(\left(y-4\right)^2-9\left(y+2\right)^2=-4\left(y +5\right)\left(2y+1\right)\)
4 tháng 12 2017
c) \(\frac{x+9}{x^2-9}+\frac{1}{x+3}=\frac{x+9}{\left(x-3\right)\left(x+3\right)}+\frac{x-3}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{x+9+x-3}{\left(x-3\right)\left(x+3\right)}=\frac{2x+6}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\frac{2}{x-3}\)
d) \(\frac{8m+8}{11n^2}.\frac{22n^2}{m^2+2m+1}\)
\(=\frac{8\left(m+1\right)}{11n^2}.\frac{22n^2}{\left(m+1\right)^2}\)
\(=\frac{8.2}{m+1}=\frac{16}{m+1}\)
e) \(\frac{5x+3}{4xy^3}:\frac{10x+6}{x^2y}\)
\(=\frac{5x+3}{4xy^3}.\frac{x^2y}{2.\left(5x+3\right)}\)
\(=\frac{x}{8y^2}\)
29 tháng 10 2017
1,Thực hiện phép tính :
a, (x + 2)9 : (x + 2)6
=(x+2)9-6
=(x+2)3
b, (x - y) 4 : (x - 2)3
=(x-y)4-3
=x-y
c, ( x2+ 2x + 4)5 : (x2 + 2x + 4)
=(x2+2x+4)5-1
=(x2+2x+4)4
d, 2(x2 + 1)3 : 1/3(x2 + 1)
=(2÷1/3).[(x2+1)3÷(x2+1)]
=6(x2+1)2
e, 5 (x - y)5 : 5/6 (x - y)2
=(5÷5/6).[(x-y)5÷(x-y)2]
=6(x-y))3
CM
4 tháng 12 2018
a) \(\left(3x-5\right)\left(2x+3\right)-\left(2x-3\right)\left(3x+7\right)-2x\left(x-4\right)\)
\(=\left(6x^2-x-15\right)-\left(6x^2+5x-21\right)-\left(2x^2-8x\right)\)
\(=6x^2-x-15-6x^2-5x+21-2x^2+8x\)
\(=-2x^2+2x+6\)
\(=-2\left(x^2-x-3\right)\)
b) \(\left(x^2+2\right)^2-\left(x+2\right)\left(x-2\right)\left(x^2+4\right)\)
\(=\left(x^2+2\right)^2-\left(x^2-4\right)\left(x^2+4\right)\)
\(=\left(x^2+2\right)^2-\left(x^4-16\right)\)
\(=\left(x^4+4x^2+4\right)-\left(x^4-16\right)\)
\(=x^4+4x^2+4-x^4+16\)
\(=4x^2+20\)
\(=4\left(x^2+5\right)\)
c) \(\left(2x-y\right)^2-2\left(x+3y\right)^2-\left(1+3x\right)\left(3x-1\right)\)
\(=\left(4x^2-4xy+y^2\right)-2\left(x^2+6xy+9y^2\right)-\left(9x^2-1\right)\)
\(=4x^2-4xy+y^2-2x^2-16xy-18y^2-9x^2+1\)
\(=-7x^2-20xy-17y^2+1\)
d) \(\left(x^2-1\right)^3-\left(x^4+x^2+1\right)\left(x^2-1\right)\)
\(=\left(x^6-3x^4+3x^2-1\right)-\left(x^6-1\right)\)
\(=x^6-3x^4+3x^2-1-x^6+1\)
\(=-3x^4+3x^2\)
\(=-3x^2\left(x^2-1\right)\)
\(=-3x^2\left(x-1\right)\left(x+1\right)\)
e) \(\left(2x-1\right)^2-2\left(4x^2-1\right)+\left(2x+1\right)^2\)
\(=\left(2x-1\right)^2-2\left(2x-1\right)\left(2x+1\right)+\left(2x+1\right)^2\)
\(=\left[\left(2x-1\right)-\left(2x+1\right)\right]^2\)
\(=\left(2x-1-2x-1\right)^2\)
\(=\left(-2\right)^2=4\)
g) \(\left(x-y+z\right)^2+\left(y-z\right)^2-2\left(x-y+z\right)\left(z-y\right)\)
\(=\left(x-y+z\right)^2+2\left(x-y+z\right)\left(y-z\right)+\left(y-z\right)^2\)
\(=\left(x-y+z+y+z\right)^2\)
\(=\left(x+2z\right)^2\)
h) \(\left(2x+3\right)^2+\left(2x+5\right)^2-\left(4x+6\right)\left(2x+5\right)\)
\(=\left(2x+3\right)^2-2\left(2x+3\right)\left(2x+5\right)+\left(2x+5\right)^2\)
\(=\left[\left(2x+3\right)-\left(2x+5\right)\right]^2\)
\(=\left(2x+3-2x-5\right)^2\)
\(=\left(-2\right)^2=4\)
i) \(5x^2-\dfrac{10x^3+15x^2-5x}{-5x}-3\left(x+1\right)\)
\(=5x^2-\dfrac{-5x\left(-2x^2-3x+1\right)}{-5x}-3\left(x+1\right)\)
\(=5x^2-\left(-2x^2-3x+1\right)-3\left(x+1\right)\)
\(=5x^2+2x^2+3x-1-3x-3\)
\(=7x^2-4\)
7 tháng 9 2022
a: \(=\dfrac{5}{2}x-2x+\dfrac{7}{2}=\dfrac{1}{2}x+\dfrac{7}{2}\)
b: \(=\dfrac{-1}{4}x^4-3x^2+\dfrac{9}{4}x\)
c: \(=\dfrac{1}{5}x+\dfrac{1}{15}xy+\dfrac{7}{10}x^2\)
d: \(=-9x^3-1-12y+27xy\)
29 tháng 6 2017
8) \(y^2-y-30=y^2+5y-6y-30=y\left(y+5\right)-6\left(y+5\right)=\left(y-6\right)\left(y+5\right)\)
9) \(y^2-8y+15=y^2-3y-5y+15=y\left(y-3\right)-5\left(y-3\right)=\left(y-5\right)\left(y-3\right)\)
10) \(y^2+y-6=y^2-2y+3y-6=y\left(y-2\right)+3\left(y-2\right)=\left(y+3\right)\left(y-2\right)\)
11) \(y^2-y-12=y^2+3y-4y-12=y\left(y+3\right)-4\left(y+3\right)=\left(y-4\right)\left(y+3\right)\)
12) \(x^2-5x+6=x^2-2x-3x+6=x\left(x-2\right)-3\left(x-2\right)=\left(x-3\right)\left(x-2\right)\)
13) \(u^2+u-42=u^2+7u-6u-42=u\left(u+7\right)-6\left(u+7\right)=\left(u-6\right)\left(u+7\right)\)
29 tháng 6 2017
14) \(2x^2+x-6=2x^2+4x-3x-6=2x\left(x+2\right)-3\left(x+2\right)=\left(2x-3\right)\left(x+2\right)\)
15) \(7x^2+50x+7=7x^2+49x+x+7=7x\left(x+7\right)+\left(x+7\right)=\left(7x+1\right)\left(x+7\right)\)
16) \(12x^2+7x-12=12x^2+16x-9x-12=4x\left(3x+4\right)-3\left(3x+4\right)=\left(4x-3\right)\left(3x+4\right)\)
17) \(15x^2+7x-2=15x^2-3x+10x-2=3x\left(5x-1\right)+2\left(5x-1\right)=\left(3x+2\right)\left(5x-1\right)\)
18) \(2x^2-y^2+xy=2x^2+2xy-xy-y^2=2x\left(x+y\right)-y\left(x+y\right)=\left(2x-y\right)\left(x+y\right)\)
19) \(x^2-3xy+2y^2=x^2-xy-2xy+2y^2=x\left(x-y\right)-2y\left(x-y\right)=\left(x-2y\right)\left(x-y\right)\)
A=x2y2+15x2y-18xy2=xy(xy+15x+18y)