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26 tháng 10 2018

Bài 1:

a) \(2x^2y-xy=xy\left(2x-1\right)\)

b)\(2x^2-x-2y^2-y=\left(2x^2-2y^2\right)-\left(x+y\right)\)

\(=2\left(x^2-y^2\right)-\left(x+y\right)\)

\(=2\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)

\(=\left(x+y\right)\left(2x-2y-1\right)\)

26 tháng 10 2018

Bài 2:

a)\(x^3-\frac{1}{9}x=0\)

\(\Leftrightarrow x\left(x^2-\frac{1}{9}\right)=0\)

\(\Leftrightarrow x\left(x-\frac{1}{3}\right)\left(x+\frac{1}{3}\right)=0\)

\(\Rightarrow x=0\text{ hoặc }x-\frac{1}{3}=0\Leftrightarrow x=\frac{1}{3}\text{ hoặc }x+\frac{1}{3}=0\Leftrightarrow x=-\frac{1}{3}\)

Vậy...

b)\(\left(x+1\right)^2=5x\left(x+1\right)\)

\(\Leftrightarrow\left(x+1\right)^2-5x\left(x+1\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(x+1-5x\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(-4x+1\right)=0\)

\(\Leftrightarrow-\left(x+1\right)\left(4x-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+1=0\\4x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-1\\4x=1\Leftrightarrow x=\frac{1}{4}\end{cases}}}\)

Vậy...

29 tháng 7 2021

1/

a)5x – 20y=5(x-4y)

b) 5x.(x –  1) –  3x(x – 1)=2x(x-1)

c) x.(x+y) – 5x – 5y=c) x.(x+y) – 5(x+y)=(x-5)(x+y)

2/

a)x2 + xy + x = x(x+y+1)=77.(77+22+1)=77.100=7700

b)  x . ( x – y ) + y . ( y – x )=(x-y)(x-y)=(x-y)2=(53-3)2=2500

3/

a) X + 5x2 = 0

⇒x(x+5)=0

⇒hoặc x=0

x+5=0⇒x=-5

b)x + 1 = ( x + 1 )2 

⇒(x + 1)-( x + 1 )2 =0

⇒x(x+1)=0

⇒ hoặc x=0

hoặc x+1=0⇒x=-1

29 tháng 7 2021

4/

a) 97 . 13 + 130 . 0,3 = 97.13+13.10.0,3=97.13+13.3=100.13=1300

b)86 . 153 – 530 . 8,6=86.153–53.10.8,6=86.153-53.86=86.100=8600

C) 85 .12,7 + 5,3 . 12,7= 12,7(85+5,3)=12,7.90,3=1146,81

D)52.143 – 52 . 39 – 8.26=52(143-39)-8,26=52.104-8,26=5399,74

1 tháng 11 2021

1.

a) \(2x^4-4x^3+2x^2\)

\(=2x^2\left(x^2-2x+1\right)\)

\(=2x^2\left(x-1\right)^2\)

b) \(2x^2-2xy+5x-5y\)

\(=\left(2x^2-2xy\right)+\left(5x-5y\right)\)

\(=2x\left(x-y\right)+5\left(x-y\right)\)

\(=\left(x-y\right)\cdot\left(2x+5\right)\)

1 tháng 11 2021

2 . 

a,

\(4x\left(x-3\right)-x+3=0\)

\(4x\left(x-3\right)-\left(x-3\right)=0\)

\(\left(x-3\right)\left(4x-1\right)=0\)

\(\left[{}\begin{matrix}x-3=0\\4x-1=0\end{matrix}\right.\)

\(\left[{}\begin{matrix}x=3\\4x=1\end{matrix}\right.\)

\(\left[{}\begin{matrix}x=3\\x=\dfrac{1}{4}\end{matrix}\right.\)

vậy \(x\in\left\{3;\dfrac{1}{4}\right\}\)

b, 

\(\)\(\left(2x-3\right)^2-\left(x+1\right)^2=0\)

\(\left(2x-3-x-1\right)\left(2x-3+x+1\right)\) = 0

\(\left(x-4\right)\left(3x-2\right)=0\)

\(\left[{}\begin{matrix}x-4=0\\3x-2=0\end{matrix}\right.\)

\(\left[{}\begin{matrix}x=4\\3x=2\end{matrix}\right.\)

\(\left[{}\begin{matrix}x=4\\x=\dfrac{2}{3}\end{matrix}\right.\)

vậy \(x\in\left\{4;\dfrac{2}{3}\right\}\)

5 tháng 8 2021
1 tháng 1 2022

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1 tháng 1 2022

a) = (x - 1)(5x - 3)

b) = x(x + y) - 5(x + y)

= (x + y)(x - 5)

c) = x(x - y) - y(x - y)

= (x - y)^2

d) = 2(x2 + 2x + 1 - y2)

= 2[(x + 1)2 - y2]

= 2(x - y + 1)(x + y + 1)

21 tháng 10 2021

a) 5(x-2y)

b) 2x(2x-1)

c) 2x(x-3y^2-4x)

d) 2(x-y)-3x(x-y)= (x-y)(2-3x)

21 tháng 10 2021

\(a,=5\left(x-2y\right)\\ b,=2x\left(2x-1\right)\\ c,=2x\left(x-3y^2-4x\right)\\ d,=\left(x-y\right)\left(2-3x\right)\)

8 tháng 3 2021

a) 3x . ( x-1 ) = 3x2 - 3x 

b) x3- 2x2+x = x2.( x-1 ) - x.( x-1 ) = (x-1).(x-1).x 

= (x-1)2.x 

c) x2- 2xy-9z2+y2

= (x2-2xy+y2 )-(3z)2

= (x-y)2-(3z)2

= ( x-y-3z).(x-y+3z)

thay vào ta có ( 6+4-90 ).(6+4+90 )=-80.100=-8000 

e) Ta có: \(x^4-2x^3+2x-1\)

\(=\left(x^4-1\right)-2x\left(x^2-1\right)\)

\(=\left(x^2+1\right)\left(x-1\right)\left(x+1\right)-2x\left(x-1\right)\left(x+1\right)\)

\(=\left(x-1\right)\left(x+1\right)\cdot\left(x^2-2x+1\right)\)

\(=\left(x+1\right)\cdot\left(x-1\right)^3\)

h) Ta có: \(3x^2-3y^2-2\left(x-y\right)^2\)

\(=3\left(x^2-y^2\right)-2\left(x-y\right)^2\)

\(=3\left(x-y\right)\left(x+y\right)-2\left(x-y\right)^2\)

\(=\left(x-y\right)\left(3x+3y-2x+2y\right)\)

\(=\left(x-y\right)\left(x+5y\right)\)

a) Ta có: \(x^2-y^2-2x-2y\)

\(=\left(x-y\right)\left(x+y\right)-2\left(x+y\right)\)

\(=\left(x+y\right)\left(x-y-2\right)\)

b) Ta có: \(x^2\left(x+2y\right)-x-2y\)

\(=\left(x+2y\right)\left(x^2-1\right)\)

\(=\left(x+2y\right)\left(x-1\right)\left(x+1\right)\)

NV
5 tháng 8 2021

a.

\(x^3-y^3+2x^2-2y^2\)

\(=\left(x-y\right)\left(x^2+xy+y^2\right)+\left(x-y\right)\left(2x+2y\right)\)

\(=\left(x-y\right)\left(x^2+xy+y^2+2x+2y\right)\)

b.

\(x^3+1-x^2-x\)

\(=\left(x+1\right)\left(x^2-x+1\right)-x\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-2x+1\right)\)

\(=\left(x+1\right)\left(x-1\right)^2\)