x2yz+5xyz-14yz
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DD
4 tháng 8 2015
=yz(x^2+5x-14)
=yz(x^2-2x+7x-14)
=yz[x(x-2)+7(x-2)
=yz(x-2)(x+7)
1 tháng 7 2019
2) \(5x^2+6xy+y^2\)
\(=9x^2+6xy+y^2-4x^2\)
\(=\left(3x+y\right)^2-\left(2x\right)^2\)
\(=\left(3x+y+2x\right)\left(3x+y-2x\right)\)
\(=\left(5x+y\right)\left(x+y\right)\)
3) \(x^2+2xy-15y^2=x^2+2xy+y^2-16y^2\)
\(=\left(x+y\right)^2-\left(4y\right)^2\)
\(=\left(x+y+4y\right)\left(x+y-4y\right)\)
\(=\left(x+5y\right)\left(x-3y\right)\)
hc tốt
4 tháng 8 2020
Bài 3:
a) Ta có: \(x^2+4xy-21y^2\)
\(=x^2+7xy-3xy-21y^2\)
\(=x\left(x+7y\right)-3y\left(x+7y\right)\)
\(=\left(x+7y\right)\left(x-3y\right)\)
b) Ta có: \(5x^2+6xy+y^2\)
\(=5x^2+5xy+xy+y^2\)
\(=5x\left(x+y\right)+y\left(x+y\right)\)
\(=\left(x+y\right)\left(5x+y\right)\)
c) Ta có: \(x^2+2xy-15y^2\)
\(=x^2+5xy-3xy-15y^2\)
\(=x\left(x+5y\right)-3y\left(x+5y\right)\)
\(=\left(x+5y\right)\left(x-3y\right)\)
d) Ta có: \(\left(x-y\right)^2+4\left(x-y\right)-12\)
\(=\left(x-y\right)^2+6\left(x-y\right)-2\left(x-y\right)-12\)
\(=\left(x-y\right)\left(x-y+6\right)-2\left(x-y+6\right)\)
\(=\left(x-y+6\right)\left(x-y-2\right)\)
e) Ta có: \(x^2-7xy+10y^2\)
\(=x^2-2xy-5xy+10y^2\)
\(=x\left(x-2y\right)-5y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x-5y\right)\)
f) Ta có: \(x^2yz+5xyz-14yz\)
\(=yz\left(x^2+5x-14\right)\)
\(=yz\left(x^2+7x-2x-14\right)\)
\(=yz\left[x\left(x+7\right)-2\left(x+7\right)\right]\)
\(=yz\left(x+7\right)\left(x-2\right)\)
30 tháng 4 2017
1) \(25x^4-10x^2y+y^2\)
\(\Leftrightarrow\left(5x^2\right)^2+2\cdot\left(5x^2\right)\cdot y+y^2\)
\(\Leftrightarrow\left(5x^2+y\right)^2\)
2) \(x^4+2x^3-4x-4\)
\(\Leftrightarrow\left(x^4-4\right)+\left(2x^3-4x\right)\Leftrightarrow\left(x^2-2\right)\left(x^2+2\right)+2x\left(x^2-2\right)\)
\(\Leftrightarrow\left(x^2-2\right)\left(x^2+2+2x\right)\)
3) \(x^4+x^2+1\)
\(\Leftrightarrow x^4+x^2-x+x+1\)
\(\Leftrightarrow\left(x^4-x\right)+\left(x^2+x+1\right)\)
\(\Leftrightarrow x\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)\(\Leftrightarrow\left(x^2+x+1\right)\left(x^2-x+1\right)\)
4) \(x^3-5x^2-14x\)\(\Leftrightarrow x^3-7x^2+2x^2-14x\)
\(\Leftrightarrow x^2\left(x-7\right)+2x\left(x-7\right)\)\(\Leftrightarrow x\left(x+2\right)\left(x-7\right)\)
5) \(x^2yz+5xyz-14yz\)\(\Leftrightarrow yz\left(x^2+5x-14\right)\)
\(\Leftrightarrow yz\left(x^2+7x-2x-14\right)\)
\(\Leftrightarrow yz\left[x\left(x+7\right)-2\left(x+7\right)\right]\)
\(\Leftrightarrow yz\left(x+7\right)\left(x-2\right)\)
CN
3
PT
1
CM
14 tháng 11 2018
Ta có: x2yz.(2xy)2z = x2yz.4x2y2.z = 4(x2.x2)(y.y2)(z.z) = 4x4y3z2
7 tháng 3 2022
Bài 4:
b: \(=x^2z\left(-1+3-7\right)=-5x^2z=-5\cdot\left(-1\right)^2\cdot\left(-2\right)=10\)
c: \(=xy^2\left(5+0.5-3\right)=2.5xy^2=2.5\cdot2\cdot1^2=5\)
NL
1
