A) 27x2.(y-1)-9x3.(1-y)
b)8x3 + 1/27
c)49.(y-4)2-9.(y+2)2
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26 tháng 10 2021
\(a,=y\left(y-2\right)\\ b,=3x\left(x^2-2x+1\right)=3x\left(x-1\right)^2\\ c,=\left(y-1\right)\left(27x^2+9x^3\right)=9x^2\left(x+3\right)\left(y-1\right)\\ d,=y\left(y^2-2y+1\right)=y\left(y-1\right)^2\\ e,=x\left(x^2+6x+9\right)=x\left(x+3\right)^2\\ f,=x\left(x^2-2xy+y^2\right)=x\left(x-y\right)^2\\ g,=\left(2-x\right)\left(x+1\right)\\ h,=\left(x-1\right)\left(3x-6\right)=3\left(x-1\right)\left(x-2\right)\)
26 tháng 10 2021
a: =y(y-2)
b: \(=3x^2\left(x^2-2x+1\right)=3x^2\left(x-1\right)^2\)
d: \(=y\left(y^2-2y+1\right)=y\left(y-1\right)^2\)
HT
29 tháng 7 2016
\(a,49.\left(y-4\right)^2-9y^2-36y-36=49\left(y-4\right)^2-9\left(y^2+4y+4\right)\)
\(=49\left(y-4\right)^2-9\left(y+4\right)^2=\left(7y-28\right)^2-\left(3y+12\right)^2\)
\(=\left(7y-28+3y+12\right)\left(7y-28-3y-12\right)\)
\(=\left(10y-16\right)\left(4y-40\right)=8\left(5y-8\right)\left(y-10\right)\)
\(b,xyz-\left(xy+yz+xz\right)+\left(x+y+z\right)-1\)
\(=xyz-xy-yz-xz+x+y+z-1\)
\(=\left(xyz-xy\right)-\left(xz-x\right)-\left(yz-y\right)+\left(z-1\right)\)
\(=xy\left(z-1\right)-x\left(z-1\right)-y\left(z-1\right)+\left(z-1\right)\)
\(=\left(z-1\right)\left(xy-x-y+1\right)\)
\(=\left(z-1\right)\text{[}x\left(y-1\right)-\left(y-1\right)\text{]}\)
\(=\left(z-1\right)\left(y-1\right)\left(x-1\right)\)
12 tháng 10 2021
\(1,\\ a,=4\left(x-2\right)^2+y\left(x-2\right)=\left(4x-8+y\right)\left(x-2\right)\\ b,=3a^2\left(x-y\right)+ab\left(x-y\right)=a\left(3a+b\right)\left(x-y\right)\\ 2,\\ a,=\left(x-y\right)\left[x\left(x-y\right)^2-y-y^2\right]\\ =\left(x-y\right)\left(x^3-2x^2y+xy^2-y-y^2\right)\\ b,=2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\\ 3,\\ a,=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\\ b,Sửa:3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\\ 4,\\ A=\left(b+3\right)\left(a-b\right)\\ A=\left(1997+3\right)\left(2003-1997\right)=2000\cdot6=12000\\ 5,\\ a,\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\\ b,\Leftrightarrow\left(x-1\right)\left(x^2-16\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\\x=-4\end{matrix}\right.\)
30 tháng 9 2016
a. 27x2 . ( y - 1 ) - 9x3 . ( 1 - y )
= 27x2 ( y - 1 ) + 9x3 ( y - 1 )
= 9x2 ( y - 1 ) ( 3 + x )
b. 8x3 + 1/27
= (2x )3 + ( 1/3 )3
= ( 2x + 1/3 ) ( 4x2 - 2/3x + 9 )
10 tháng 8 2021
a, \(\left(x+1\right)^2-25=\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)
b, \(\left(xy+4\right)^2-4\left(x+y\right)^2=\left(xy+4\right)^2-\left(2x+2y\right)^2=\left(xy+4-2x-2y\right)\left(xy+4+2x+2y\right)\)
c, xem lại đề nhé
NH
3
15 tháng 9 2021
1) \(x\sqrt{y}+y\sqrt{x}=\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)\)
2) \(9-6\sqrt{a}+a=\left(\sqrt{a}-3\right)^2\)
3) \(a+2\sqrt{ab}+b=\left(\sqrt{a}+\sqrt{b}\right)^2\)
4) \(x-y+\sqrt{x}+\sqrt{y}=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)+\left(\sqrt{x}+\sqrt{y}\right)=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}+1\right)\)
5) \(a+2\sqrt{ab}+b-1=\left(\sqrt{a}+\sqrt{b}\right)^2-1=\left(\sqrt{a}+\sqrt{b}-1\right)\left(\sqrt{a}+\sqrt{b}+1\right)\)
15 tháng 9 2021
1) \(x\sqrt{y}+y\sqrt{x}=\sqrt{x}\sqrt{y}\left(\sqrt{x}+\sqrt{y}\right)\)
2) \(9-6\sqrt{a}+a=\left(3-\sqrt{a}\right)^2\)
3) \(a+2\sqrt{ab}+b=\left(\sqrt{a}+\sqrt{b}\right)^2\)
4) \(x-y+\sqrt{x}+\sqrt{y}=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)+\left(\sqrt{x}+\sqrt{y}\right)=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}+1\right)\)
5) \(a+2\sqrt{ab}+b-1=\left(\sqrt{a}+\sqrt{b}\right)^2-1^2=\left(\sqrt{a}+\sqrt{b}-1\right)\left(\sqrt{a}+\sqrt{b}+1\right)\)
a)27x2.(y-1)9x3.(1-y)
=27x2.(y-1)+9x3.(y-1)
=9x2(y-1)[3+x]
b)8x3 + 1/27
=(2x)3 + (\(\frac{1}{3}\))3
= (2x+\(\frac{1}{3}\))(\(\left(2x\right)^2-\frac{2}{3}x+\left(\frac{1}{3}\right)^2\)
= (2x+\(\frac{1}{3}\))(\(\left(2x\right)^2-\frac{2}{3}x+\left(\frac{1}{3}\right)^2\)
a) 27x2 ( y - 1) - 9x3 ( 1 - y)
=27x2 (y-1) + 9x3 ( y - 1 )
= (27x2 + 9x3) ( y -1 )
=9x2 ( x + 3) ( y - 1)
b)8x3+1/27
\(=\left(2x\right)^3+\left(\frac{1}{3}\right)^3\)
\(=\left(\frac{2x}{9}+\frac{1}{27}\right)\left(36x^2-6x+1\right)\)
c)49 ( y - 4 )2 - 9 ( y + 2)2
= [7(y - 4)]2 - [3(y + 2)]2
= (7y - 28 + 3y + 6)(7y - 28 - 3y - 6)
= (10y - 22)(4y - 34)
= 4(5y - 11)(2y - 34)