Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
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-\(\dfrac{3xy}{2}\)+\(\dfrac{y^2}{4}\))
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)
Bài 1:
a)\(5x^2y^3-25x^3y^4+10x^3y^3=5x^2y^3\left(1-5xy+2x\right)\)
b)\(x^3-2xy-x^2y+2y^2=\left(x^3-x^2y\right)-\left(2xy-2y^2\right)=x^2\left(x-y\right)-2y\left(x-y\right)=\left(x-y\right)\left(x^2-2y\right)\)
c)Đề sai hoàn toàn
d) \(2x^2+4xy+2y^2-8z^2=2\left(x^2+2xy+y^2-4z^2\right)=2\left[\left(x+y\right)^2-\left(2z\right)^2\right]=2\left(x+y-2z\right)\left(x+y+2z\right)\)e) \(3x-3a+yx-ya=3\left(x-a\right)+y\left(x-a\right)=\left(x-a\right)\left(3+y\right)\)
f)\(\left(x^2+y^2\right)^2-4x^2y^2=\left(x-y\right)^2\left(x+y\right)^2\)
g)\(2x^2-5x+2=2x^2-x-4x+2=x\left(2x-1\right)-2\left(2x-1\right)=\left(2x-1\right)\left(x-2\right)\)
i)\(14x\left(x-y\right)-21y\left(y-x\right)+28z\left(x-y\right)=14x\left(x-y\right)+21y\left(x-y\right)+28z\left(x-y\right)=7\left(x-y\right)\left(2x+3y+4z\right)\)
a ) 36x2 - ( 3x - 2 )2
= ( 6x - 3x + 2 ) ( 6x + 3x - 2 )
= ( 3x + 2 ) ( 9x - 2 )
b ) 16.( 4x + 5 )2 - 25. ( 2x + 2 )2
= [ 4.( 4x + 5 ) + 5. ( 2x + 2 ) ] [ 4 .( 4x + 5 ) - 5. ( 2x + 2 ) ]
= ( 16x + 5 + 10x + 10 ) ( 16x + 5 - 10x - 10 )
= ( 26x + 15 ) ( 6x - 5 )
a ) 36x2 - ( 3x - 2 )2
= ( 6x - 3x + 2 ) ( 6x + 3x - 2 )
= ( 3x + 2 ) ( 9x - 2 )
b ) 16.( 4x + 5 )2 - 25. ( 2x + 2 )2
= [ 4.( 4x + 5 ) + 5. ( 2x + 2 ) ] [ 4 .( 4x + 5 ) - 5. ( 2x + 2 ) ]
= ( 16x + 5 + 10x + 10 ) ( 16x + 5 - 10x - 10 )
= ( 26x + 15 ) ( 6x - 5 )
b) \(-y^8+10y^4x^3-25x^6\)
\(=-\left(y^8-10y^4x^3+25x^6\right)\)
\(=-\left[\left(y^4\right)^2-2.y^4.5x^3+\left(5x^3\right)^2\right]\)
\(=-\left(y^4-5x^3\right)^2\)
c) \(8x^3+36x^2y+54xy^2+27y^3\)
\(=\left(2x\right)^3+3.\left(2x\right)^2.3y+3.2x.\left(3y\right)^2+\left(3y\right)^3\)
\(=\left(2x+3y\right)^3\)
d) \(-y^3+12y^2x-48yx^2+64x^3\)
\(=-\left(y^3-12y^2x+48yx^2-64x^3\right)\)
\(=-\left[y^3-3.y^2.4x+3.y.\left(4x\right)^2-\left(4x\right)^3\right]\)
\(=-\left(y-4x\right)^3\)
e) \(64x^6y^4-81x^2y^2\)
\(=\left(8x^3y^2\right)^2-\left(9xy\right)^2\)
\(=\left(8x^3y^2-9xy\right)\left(8x^3y^2+9xy\right)\)
f) \(64x^6-27y^6\)
\(=\left(4x^2\right)^3-\left(3y^2\right)^3\)
\(=\left(4x^2-3y^2\right)\left[\left(4x^2\right)^2+4x^2.3y^2+\left(3y^2\right)^2\right]\)
\(=\left(4x^2-3y^2\right)\left(16x^4+12x^2y^2+9x^4\right)\)
a. 6x3y2 ( 2-x) + 9x2y2 (x-2)
= -6x3y2 (x-2) + 9x2y2 ( x-2)
= (x-2) 3x2y2 ( -2x + 3)
b. x2 - 4x + 4y - y2
= x2 - y2 - (4x - 4y )
= (x-y)(x+y) - 4( x-y)
= (x-y)(x+y-4)
c. 81x2 + 6yz -9y2-z2
= 81x2 - (9y2 - 6yz + z2 )
= (9x)2 - ( 3y - z )2
= (9x + 3y -z)(9x - 3y + z )
\(a,=6x^3y^2\left(2-x\right)-9x^2y^2\left(2-x\right)\)
\(=\left(2-x\right)\left(6x^3y^2-9x^2y^2\right)=\left(2-x\right)3x^2y^2\left(2x-3\right)\)
\(f,=\left(x-3-x-2\right)\left(x-3+x+2\right)\)
\(=-5\left(2x-1\right)\)
\(g,=\left(x-3\right)\left(x+3\right)+2\left(x+3\right)\)
\(=\left(x+3\right)\left(x-3+2\right)\)
\(=\left(x+3\right)\left(x-1\right)\)
a) 5x ( x - 2000 ) - x + 2000 = 0
5x ( x - 2000 ) - ( x - 2000 ) = 0
5x ( x - 2000 ) = 0
\(\Rightarrow\orbr{\begin{cases}5x=0\\x-2000=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=2000\end{cases}}\)
Vậy ....
b) x3 - 13x = 0
x ( x2 - 13 ) = 0
x ( x - \(\sqrt{13}\)) - ( x + \(\sqrt{13}\)) = 0
\(\Rightarrow\hept{\begin{cases}x=0\\x-\sqrt{13}\\x+\sqrt{13}\end{cases}}\Rightarrow\hept{\begin{cases}x=0\\x=\sqrt{13}\\x=\sqrt{-13}\end{cases}}\)
Vậy ....
a) x2 + 6 + 9
= x2 + 2 . 3 . x + 32
= ( x + 3 )2
b) 10x - 25 - x2
= - ( x2 - 10x + 25 )
= - ( x - 5 )2
c) 8x3 - 1/8
= ( 2x )3 - ( 1/2 )3
= ( 2x - 1/2 ) ( 4x2 + x + 1/4 )
d) 1/25 x2 - 64x2
= ( 1/5x )2 - ( 8x )2
= ( 1/5x + 8x ) ( 1/5 - 8x )
\(x^3-13x=0\)
<=> \(x\left(x^2-13\right)=0\)
<=> \(x\left(x-\sqrt{13}\right)\left(x+\sqrt{13}\right)=0\)
<=> \(x=0\)
hoặc \(x-\sqrt{13}=0\)
hoặc \(x+\sqrt{13}=0\)
<=> .....
Bài 2:
a: \(A=\left(2x-y\right)^2=\left(12-2\right)^2=100\)
b: \(=\left(x-3\right)^3=100^3=1000000\)
c: \(=\left(x-y\right)^2-9z^2\)
\(=\left(x-y-3z\right)\left(x-y+3z\right)\)
\(=\left(6+4-90\right)\left(6+4+90\right)=-80\cdot100=-8000\)
a) 10x(x - y)2 - 5(x - y)3 = [10x - 5(x - y)](x - y)2 = (10x - 5x + y)(x - y)2 = (5x + y)(x - y)2
b) -x2 - 10x - 25 = -(x2 + 10x + 52) = -(x + 5)2
c) 64x6y4 - 81x2y2 = (8x3y2)2 - (9xy)2 = (8x3y2 + 9xy)(8x3y2 - 9xy)
d) x6 - y6 = (x3)2 - (y3)2 = (x3 - y3)(x3 + y3) = (x - y)(x2 + xy + y2)(x + y)(x2 - xy + y2)
e)1/8x3 - 3/4x2y + 3/2xy2 - y3 = (1/2x)3 - 3.(1/2x)2y + 3.1/2xy2 - y3 = (1/2x - y)3
f) (3x + 1)2 - (x - 1)2 = (3x + 1 + x - 1)(3x + 1 - x + 1) = 4x(2x + 2) = 8x(x + 1)