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22 tháng 9 2017
a) -25x6 - y8 + 10x3y4 = -25x6 + 10x3y4 - y8
= - ( 25x6 - 10x3y4 + y8 )
= - [ ( 5x3 )2 - 2 . 5x3y4 + ( y4 )2 ]
= - ( 5x3 - y4 )2
b) \(\dfrac{1}{4}\)x2 - 5xy + 25y2 = (\(\dfrac{1}{2}\)x)2 - 2 . \(\dfrac{1}{2}\) x . 5y + ( 5y )2
= (\(\dfrac{1}{2}\) x - 5y )2
c) ( x - 5 )2 - 16 = ( x - 5 )2 - 42
= ( x - 5 - 4 ) . ( x - 5 + 4 )
= ( x - 9 ) . ( x - 1 )
d) 25 - ( 3 - x )2 = 52 - ( 3 - x )2
= ( 5 - 3 + x ) . ( 5 + 3 - x )
= ( x + 2 ) . ( 8 - x )
KK
23 tháng 9 2017
bai 3
a) 36-12x+x2
= x2-12x+36
=(x-6)2
b) 4x2+12x+9
=(2x+3)2
c) -25x6-y8+10x3y4
=-(25x6+y8-10x3y4)
=-(5x3)2+(y4)2-10x3y4
=-(5x3)2-2.5x3y4+(y4)
=-(5x3-y4)2
d) \(\dfrac{1}{4}\) x2-5xy+25y2
=(\(\dfrac{1}{2}\) x-5y)2
23 tháng 9 2017
Bài3:
Bạn =kia làm r nhé
Bài4:
\(a,75^2-25^2\\ =\left(75-25\right)\left(75+25\right)\\ =50.100=5000\\ b,53^2-47^2\\ =\left(53-47\right)\left(53+47\right)\\ =6.100=600\\ c,31,8^2-2.31,8.21,8+21,8^2\\ =\left(31,8-21,8\right)^2\\ =10^2=100\\ d,58,2+2.58,2.41,8+41,8^2\\ =\left(58,2+41,8\right)^2\\ =100^2=1000\)
18 tháng 8 2018
Bài 8:
b. 1+8x6y3 = 13+23(x2)3y3 = 13+(2x2y)3
= (1+2x2y)(1-2x2y+4x4y2)
e. 27x3+\(\dfrac{y^3}{8}\)\(=\left(3x\right)^3+\left(\dfrac{y}{2}\right)^3\)
= (3x+\(\dfrac{y}{2}\))(9x2-\(\dfrac{3xy}{2}\)+\(\dfrac{y^2}{4}\))
18 tháng 8 2018
Bài 9:
c. 1- 9x +27x2 -27x3 = 13-3.12.3x+3.(3x)2-(3x)3
= (1-3x)3
d. x3+\(\dfrac{3}{2}x^2\)+\(\dfrac{3}{4}x+\dfrac{1}{8}\) = x3+\(3x^2.\dfrac{1}{2}\)+\(3x.\dfrac{1}{4}+\left(\dfrac{1}{2}\right)^3\)
= (x+\(\dfrac{1}{2}\))3
f. x2 - 2xy +y2 -4m2 +4m.n - n2 = (x2 - 2xy +y2)-((2m)2 -2.2m.n + n2)
= (x-y)2-(2m-n)2 = (x-y-2m+n)(x-y+2m-n)
KT
24 tháng 7 2018
\(5x^2y^3-25x^2y^2+10x^2y^4=5x^2y^2\left(y-5+2y^2\right)\)
\(12a^4-24a^2b^2-6ab=6a\left(2a^3-4ab^2-3b\right)\)
mk chỉnh đề
\(-25x^6-y^8+10x^3y^4=-\left(5x^3-y^4\right)^2\)
\(25-\left(3-x\right)^2=\left(5-3+x\right)\left(5+3-x\right)=\left(2+x\right)\left(8-x\right)\)
DN
20 tháng 8 2018
Bài 14:Tìm x
a,\(x-3=\left(3-x\right)^2\)
\(\Rightarrow\left(x-3\right)-\left(3-x\right)^2=0\)
\(\Rightarrow\left(x-3\right)+\left(x-3\right)^2=0\)
\(\Rightarrow\left(x-3\right)\left(1+x-3\right)=0\)
\(\Rightarrow\left(x-3\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\x-2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=2\end{matrix}\right.\)
b,\(\left(2x-5\right)-\left(5+2x\right)^2=0\)
\(\Rightarrow\left(2x-5\right)+\left(2x-5\right)^2=0\)
\(\Rightarrow\left(2x-5\right)\left(1+2x-5\right)=0\)
\(\Rightarrow\left(2x-5\right)\left(2x-4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}2x-5=0\\2x-4=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=5\\2x=4\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=2\end{matrix}\right.\)
23 tháng 12 2018
a) 4x2y3.\(\dfrac{2}{4}\)x3y
= (4.\(\dfrac{2}{4}\))(x2.x3)(y3.y)
=\(\dfrac{1}{2}\)x5y4
b)(5x-2)(25x2+10x+4)
=(5x-2)(5x+2)2
= (5x-2)(5x+2)(5x+2)
=(5x2-22)(5x+2)
QN
23 tháng 12 2018
a) 4x2y3 .2/4x3y
= 2x5y4
b) (5x-2)(25x2+10x+4)
= 125x3+50x2+20x-50x2-20x-8.
= 125x3-8
1 tháng 8 2017
\(1.\)
\(x^3z+x^2yz-x^2z^2-xyz^2\)
\(=x^3z-x^2z^2+x^2yz-xyz^2\)
\(=x^2z\left(x-z\right)-xyz\left(x-z\right)\)
\(=\left(x^2z-xyz\right)\left(x-z\right)\)
\(=xz\left(x-y\right)\left(x-z\right)\)
\(2.\)
\(x^2-\left(a+b\right)xy+aby^2\)
\(=x^2-axy-bxy+aby^2\)
\(=x^2-bxy-axy+aby^2\)
\(=x\left(x-by\right)-ay\left(x-by\right)\)
\(=\left(x-ay\right)\left(x-by\right)\)
\(3.\)
\(ab\left(x^2+y^2\right)+xy\left(x^2+y^2\right)\)
\(=abx^2+aby^2+a^2xy+b^2xy\)
\(=abx^2+b^2xy+a^2xy+aby^2\)
\(=bx\left(ax+by\right)+ay\left(ax+by\right)\)
\(=\left(ax+by\right)\left(bx+ay\right)\)
\(4.\)
\(\left(xy+ab\right)^2+\left(ay-bx\right)^2\)
\(=x^2y^2+2abxy+a^2b^2+a^2y^2-2aybx+b^2x^2\)
\(=x^2y^2+a^2b^2+a^2y^2+b^2x^2\)
\(=x^2y^2+b^2x^2+a^2b^2+a^2y^2\)
\(=x^2\left(b^2+y^2\right)+a^2\left(b^2+y^2\right)\)
\(=\left(a^2+x^2\right)\left(b^2+y^2\right)\)
\(5.\)
\(a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)\)
\(=a^2b-a^2c+b^2c-ab^2+ac^2-bc^2\)
\(=a^2b-ab^2-a^2c-b^2c+ac^2-bc^2\)
\(=ab\left(a-b\right)-c\left(a^2-b^2\right)+c^2\left(a-b\right)\)
\(=ab\left(a-b\right)-c\left(a-b\right)\left(a+b\right)+c^2\left(a-b\right)\)
\(=\left(a-b\right)\left(ab-ac-bc+c^2\right)\)
\(=\left(a-b\right)\left(ab-bc-ac+c^2\right)\)
\(=\left(a-b\right)\left[b\left(a-c\right)-c\left(a-c\right)\right]\)
\(=\left(a-c\right)\left(b-c\right)\left(a-c\right)\)
\(=\left(a-b\right)\left(a-c\right)\left(b-c\right)\)
\(6.\)
\(16x^2-40xy+2y^2\)
\(=\left(4x\right)^2-2\cdot4\cdot5xy+\left(5y\right)^2\)
\(=\left(4x-5y\right)^2\)
\(7.\)
\(25x^4-10x^2y+y^2\)
\(=\left(5x^2\right)^2-2\cdot5x^2y+y^2\)
\(=\left(5x^2+y\right)^2\)
\(8.\)
\(-16x^4y^6-24x^5y^5-9x^6y^4\)
\(=-\left(4^2x^4y^6+2\cdot4\cdot3x^5y^5+3^2x^6y^4\right)\)
\(=-\left[\left(4x^2y^3\right)^2+2\left(4x^2y^3\right)\left(3x^3y^2\right)+\left(3x^3y^2\right)^2\right]\)
\(=\left(4x^2y^3+3x^3y^2\right)^2\)
\(9.\)
\(16x^2-4y^2-8x+1\)
\(=\left(4x\right)^2-\left(2y\right)^2-8x+1\)
\(=\left(4x\right)^2-8x+1-\left(2y\right)^2\)
\(=\left(4x+1\right)^2-\left(2y\right)^2\)
\(=\left(4x-2y+1\right)\left(4x+2y+1\right)\)
\(10.\)
\(49x^2-25+42xy+9y^2\)
\(=\left(7x\right)^2-5^2+2\cdot7\cdot3xy+\left(3y\right)^2\)
\(=\left(7x\right)^2+2\cdot7\cdot3xy+\left(3y\right)^2-5^2\)
\(=\left(7x+3y\right)^2-5^2\)
\(=\left(7x+5y+5\right)\left(7x+3y-5\right)\)
b: \(=\left(\dfrac{1}{2}x-5y\right)^2\)