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17 tháng 9 2023

a) \(({x^2} + 2x + 3) + (3{x^2} - 5x + 1) = ({x^2} + 3{x^2}) + (2x - 5x) + (3 + 1) = 4{x^2} - 3x + 4\);        

b) \(\begin{array}{l}(4{x^3} - 2{x^2} - 6) - ({x^3} - 7{x^2} + x - 5) = 4{x^3} - 2{x^2} - 6 - {x^3} + 7{x^2} - x + 5\\ = (4{x^3} - {x^3}) + ( - 2{x^2} + 7{x^2}) - x + ( - 6 + 5) = 3{x^3} + 5{x^2} - x - 1\end{array}\);

c) \(\begin{array}{l} - 3{x^2}(6{x^2} - 8x + 1) =  - 3{x^2}.6{x^2} -  - 3{x^2}.8x +  - 3{x^2}.1\\ =  - 18{x^{2 + 2}} + 24{x^{2 + 1}} - 3{x^2} =  - 18{x^4} + 24{x^3} - 3{x^2}\end{array}\);               

d) \(\begin{array}{l}(4{x^2} + 2x + 1)(2x - 1) = (4{x^2} + 2x + 1).2x - (4{x^2} + 2x + 1).1 = 4{x^2}.2x + 2x.2x + 1.2x - 4{x^2} - 2x - 1\\ = 8{x^{2 + 1}} + 4{x^{1 + 1}} + 2x - 4{x^2} - 2x - 1 = 8{x^3} + 4{x^2} + 2x - 4{x^2} - 2x - 1 = 8{x^3} - 1\end{array}\);

e) \(\begin{array}{l}({x^6} - 2{x^4} + {x^2}):( - 2{x^2}) = {x^6}:( - 2{x^2}) - 2{x^4}:( - 2{x^2}) + {x^2}:( - 2{x^2})\\ =  - \dfrac{1}{2}{x^{6 - 2}} + {x^{4 - 2}} - \dfrac{1}{2}{x^{2 - 2}} =  - \dfrac{1}{2}{x^4} + {x^2} - \dfrac{1}{2}.\end{array}\);  

g) 

 \(({x^5} - {x^4} - 2{x^3}):({x^2} + x)=x^3-2x^2\)

a: =1/2x^3*x^2-1/2x^3*6x-1/2x^3*10

=1/2x^5-3x^4-5x^3

b: =-3x^2*5x^3+3x^2*4x^2-3x^2*3x+3x^2*3x

=-15x^5+12x^4-9x^3+9x^2

c: \(=3x\cdot5x^2-3x\cdot2x-3x=15x^3-6x^2-3x\)

d: \(=\dfrac{1}{2}x^2y\cdot2x^3-\dfrac{1}{2}x^2y\cdot\dfrac{2}{5}xy^2-\dfrac{1}{2}x^2y=x^5y-\dfrac{1}{5}x^3y^3-\dfrac{1}{2}x^2y\)

23 tháng 9 2023

\(\dfrac{2x+4}{x^3-1}-\dfrac{2}{x-1}+\dfrac{x+2}{x^2+x+1}\\ =\dfrac{2x+4}{\left(x-1\right)\left(x^2+x+1\right)}-\dfrac{2}{x-1}+\dfrac{x+2}{x^2+x+1}\\ =\dfrac{2x+4}{\left(x-1\right)\left(x^2+x+1\right)}-\dfrac{2\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{\left(x+2\right)\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\\ =\dfrac{2x+4-2x^2-2x-2+x^2-x+2x-2}{\left(x-1\right)\left(x^2+x+1\right)}\\ =\dfrac{-x^2+x}{\left(x-1\right)\left(x^2+x+1\right)}\\ =\dfrac{-x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)

\(=-\dfrac{x}{x^2+x+1}\)

23 tháng 9 2023

`a, 2/(x+1)` hay `2/(x-1)` cậu nhỉ?

`b,`

\(\dfrac{x-1}{x^2-5x+6}-\dfrac{x-3}{x-2}+\dfrac{x-2}{x-3}\\ =\dfrac{x-1}{\left(x-2\right)\left(x-3\right)}-\dfrac{x-3}{x-2}+\dfrac{x-2}{x-3}\\ =\dfrac{x-1}{\left(x-2\right)\left(x-3\right)}-\dfrac{\left(x-3\right)^2}{\left(x-2\right)\left(x-3\right)}+\dfrac{\left(x-2\right)^2}{\left(x-3\right)\left(x-2\right)}\\ =\dfrac{x-1-\left(x^2-6x+9\right)+x^2-4x+4}{\left(x-2\right)\left(x-3\right)}\\ =\dfrac{x-1-x^2+6x-9+x^2-4x+4}{\left(x-2\right)\left(x-3\right)}\\ =\dfrac{3x-6}{\left(x-2\right)\left(x-3\right)}\)

\(=\dfrac{3\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}\\ =\dfrac{3}{x-3}\)

Tham khảo

a)

-7x2(3x - 4y)

= -7x2.3x + 7x.4y

= -21x2 + 28x2y

b)

(x - 3)(5x - 4)

= x.5x - x.4 - 3.5x + 3.4

= 5x2 - 4x - 15x + 12

= 5x2 - 19x + 12

c)

(2x - 1)2 = 4x2 - 4x + 1

d)

(x + 3)(x - 3) = x2 - 32 = x2 - 9

8 tháng 12 2021

a, = -21x3 +28x2y

b, = 5x2 -4x -15x +12

= 5x2 -19x +12

c, =x2 -9

a: \(=\dfrac{x^5}{3x}+\dfrac{12x^2}{3x}+\dfrac{5x}{3x}=\dfrac{1}{3}x^4+4x+\dfrac{5}{3}\)

b: \(=\dfrac{-5x^4}{-5x}-\dfrac{15x^3}{5x}+\dfrac{18x}{5x}=x^3-3x^2+\dfrac{18}{5}\)

c: \(=\dfrac{-x^6}{0.5x}+\dfrac{5x^4}{0.5x}-\dfrac{2x^3}{0.5x}=-2x^5+10x^3-4x^2\)

18 tháng 12 2021

Bài 1:

\(a,=6x^2+6x\\ b,=15x^3-10x^2+5x\\ c,=6x^3+12x^2\\ d,=15x^4+20x^3-5x^2\\ e,=2x^2+3x-2x-3=2x^2+x-3\\ f,=3x^2-5x+6x-10=3x^2+x-10\)

Bài 2:

\(a,\Leftrightarrow3x^2+3x-3x^2=6\\ \Leftrightarrow3x=6\Leftrightarrow x=2\\ b,\Leftrightarrow6x^2+3x-6x^2+9x-2x-3=10\\ \Leftrightarrow10x=13\Leftrightarrow x=\dfrac{13}{10}\)

10 tháng 12 2021

\(a,=-21x^3+28x^2y\\ b,=5x^2-4x-15x+12=5x^2-19x+12\\ c,=4x^2-4x+1\\ d,=49-x^2\)

HQ
Hà Quang Minh
Giáo viên
17 tháng 9 2023

a)

\(\begin{array}{l}R(x) + S(x) =  - 8{x^4} + 6{x^3} + 2{x^2} - 5x + 1 + {x^4} - 8{x^3} + 2x + 3\\ = ( - 8 + 1){x^4} + (6 - 8){x^3} + 2{x^2} + ( - 5 + 2)x + (1 + 3)\\ =  - 7{x^4} - 2{x^3} + 2x - 3x + 4\end{array}\)

b)

\(\begin{array}{l}R(x) - S(x) =  - 8{x^4} + 6{x^3} + 2{x^2} - 5x + 1 - ({x^4} - 8{x^3} + 2x + 3)\\ =  - 8{x^4} + 6{x^3} + 2{x^2} - 5x + 1 - {x^4} + 8{x^3} - 2x - 3\\ = ( - 8 - 1){x^4} + (6 + 8){x^3} + 2{x^2} + ( - 5 - 2)x + (1 - 3)\\ =  - 9{x^4} + 14{x^3} + 2x - 7x - 2\end{array}\)

16 tháng 4 2022

a) x-y

b) 8x2+x

c) 1

17 tháng 11 2021

\(1,\\ a,=2x^2+2x\\ b,=x^2+4x+3-4=x^2+4x-1\\ c,=x^2+4x+4+3x-5=x^2+7x-1\\ 2,\\ a,=3\left(x+y\right)\\ b,=\left(x-3\right)^2\\ c,=7\left(x+y\right)\\ 3,\\ \Leftrightarrow\left(x-1\right)\left(3x-5\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{5}{3}\end{matrix}\right.\)

17 tháng 11 2021

a) 2x2+2x