Thực hiện phép tính
a) \(6x^n.\left(x^2-1\right)+2x.\left(3x^{n-1}+1\right)\)
b) \(3^{n+1}-2.3^n\)
c) \(3^{10}.2^{10}-6^7.\left(6^3-1\right)\)
Những câu hỏi liên quan
Thực hiện phép tính :
a, \(^{6x^n.\left(x^2-1\right)+2x.\left(3x^{n-1}+1\right)}\)
b, \(3x^{n-2}.\left(x^{n+2}y^{n+2}\right)+y^{n+2}.\left(3x^{n-2}-y^{n-2}\right)\)
c, \(4x^{n+1}-3.4^n\)
d, \(6^2.3^8.2^8-6^5.\left(6^{5-1}\right)\)
Bài 2 . Thực hiện phép tính
a)\(6x^3\)\(\left(\dfrac{1}{3}x^2-\dfrac{5}{2}-\dfrac{1}{6}\right)\)\(-2x^5\)\(-x^3\)
b)\(\left(x-3\right)\left(x^2+3x-2\right)\)
c)\(\left(4x^3-4x^2-5x+4\right):\left(2x+1\right)\)
a: =2x^5-15x^3-x^2-2x^5-x^3=-16x^3-x^2
b: =x^3+3x^2-2x-3x^2-9x+6
=x^3-11x+6
c: \(=\dfrac{4x^3+2x^2-6x^2-3x-2x-1+5}{2x+1}\)
\(=2x^2-3x-1+\dfrac{5}{2x+1}\)
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a) \(6x^3\left(\dfrac{1}{3}x^2-\dfrac{5}{2}-\dfrac{1}{6}\right)-2x^5-x^3\)
\(=6x^3\left(\dfrac{1}{3}x^2-\dfrac{16}{6}\right)-2x^5-x^3\)
\(=2x^5-16x^3-2x^5-x^3\)
\(=-17x^3\)
b) \(\left(x+3\right)\left(x^2+3x-2\right)\)
\(=x^3+3x^2-2x+3x^2+9x-6\)
\(=x^3+6x^2+7x-6\)
c) \(\left(4x^3-4x^2-5x+4\right):\left(2x+1\right)\)
\(=2x^2+4x^3-2x-4x^2-\dfrac{5}{2}-5x+\dfrac{2}{x}+4\)
\(=4x^3-2x^2-7x+\dfrac{2}{x}+\dfrac{3}{2}\)
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Rút gọn
a) \(3^{10}.2^{10}-6^7.\left(6^3-1\right)\)
b) \(2x^n.\left(3x^{n+1}-1\right)-3x^{n+1}.\left(2x^n-1\right)\)
11 tháng 11 2021 lúc 21:28
thực hiện phép tính
a) \(\left(x-7\right)\left(x+5\right)\)
b) \(\left(xy-1\right)\left(xy+5\right)\)
c) \(\left(x^3-2x^2+x-1\right)\left(5-x\right)\)
a: \(=x^2-2x-35\)
b: \(=x^2y^2+4xy-5\)
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a) \(=x^2-7x+5x-35=x^2-2x-35\)
b) \(=x^2y^2-xy+5xy-5=x^2y^2+4xy-5\)
c) \(=5x^3-10x^2+5x-5-x^4+2x^3-x^2+x=7x^3-x^4-11x^2+6x-5\)
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Xem thêm câu trả lời
Tìm các số nguyên x sao cho tích của 2 số hữu tỉ -dfrac{3}{x-1};dfrac{x-2}{2} là một số nguyên
Giải :
Ta có :
-dfrac{3}{x-1}.dfrac{x-2}{2}dfrac{-3left(x-2right)}{left(x-1right).2}dfrac{-3x+6}{2x-2}
dfrac{-3x+6}{2x-2} là một số nguyên khi -3x+6⋮2x-2
Leftrightarrow2left(-3x+6right)+3left(2x-2right)⋮2x-2
Leftrightarrow-6x+12+6x-6⋮2x-2
Leftrightarrowleft(-6x+6xright)+left(12-6right)⋮2x-2
Leftrightarrow6⋮2x-2
Leftrightarrow2x-2inƯleft(6right)left{1;-1;2;-2;3;-3;6;-6right}
Leftrightarrow2xinle...
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Tìm các số nguyên x sao cho tích của 2 số hữu tỉ \(-\dfrac{3}{x-1};\dfrac{x-2}{2}\) là một số nguyên
Giải :
Ta có :
\(-\dfrac{3}{x-1}.\dfrac{x-2}{2}=\dfrac{-3\left(x-2\right)}{\left(x-1\right).2}=\dfrac{-3x+6}{2x-2}\)
\(\dfrac{-3x+6}{2x-2}\) là một số nguyên khi \(-3x+6⋮2x-2\)
\(\Leftrightarrow2\left(-3x+6\right)+3\left(2x-2\right)⋮2x-2\\ \Leftrightarrow-6x+12+6x-6⋮2x-2\\ \Leftrightarrow\left(-6x+6x\right)+\left(12-6\right)⋮2x-2\\ \Leftrightarrow6⋮2x-2\\ \Leftrightarrow2x-2\inƯ\left(6\right)=\left\{1;-1;2;-2;3;-3;6;-6\right\}\\ \Leftrightarrow2x\in\left\{3;1;4;0;5;-1;8;-4\right\}\\ \Leftrightarrow x\in\left\{2;0;4;-2\right\}\)
thực hiện phép tính
\(3x^n\left(6x^{n-3}+1\right)-2x^n\left(9x^{n-3}-1\right)\))
\(3x^n\left(6x^{n-3}+1\right)-2x^n\left(9x^{n-3}-1\right)\)
\(=18x^{2n-3}+3x^n-18x^{2n-3}+2x^n\)
\(=3x^n+2x^n\)
\(=5x^n\)
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25 tháng 2 2023 lúc 14:53
Bài `1`: Rút gọn các biểu thức sau:a)4x^2left(5x^2+3right)-6xleft(3x^3-2x+1right)-5x^3left(2x-1right)b)dfrac{3}{2}xleft(x^2-dfrac{2}{3}x+2right)-dfrac{5}{3}x^2left(x+dfrac{6}{5}right)Bài `2`: Thực hiện các phép nhân sau:a)left(x^2-xright)cdotleft(2x^2-x-10right)b)left(0,2x^2-3xright)cdot5left(x^2-7x+3right)c)6x^2cdotleft(2x^3-3x^2+5x-4right)d)left(-1,2x^2right)cdotleft(2,5x^4-2x^3+x^2-1,5right)
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Bài `1`: Rút gọn các biểu thức sau:
\(a)4x^2\left(5x^2+3\right)-6x\left(3x^3-2x+1\right)-5x^3\left(2x-1\right)\)
\(b)\dfrac{3}{2}x\left(x^2-\dfrac{2}{3}x+2\right)-\dfrac{5}{3}x^2\left(x+\dfrac{6}{5}\right)\)
Bài `2`: Thực hiện các phép nhân sau:
\(a)\left(x^2-x\right)\cdot\left(2x^2-x-10\right)\)
\(b)\left(0,2x^2-3x\right)\cdot5\left(x^2-7x+3\right)\)
\(c)6x^2\cdot\left(2x^3-3x^2+5x-4\right)\)
\(d)\left(-1,2x^2\right)\cdot\left(2,5x^4-2x^3+x^2-1,5\right)\)
Bài 2:
a: \(=2x^4-x^3-10x^2-2x^3+x^2+10x=2x^3-3x^3-9x^2+10x\)
b: \(=\left(x^2-15x\right)\left(x^2-7x+3\right)\)
\(=x^4-7x^3+3x^2-15x^3+105x^2-45x\)
\(=x^4-22x^3+108x^2-45x\)
c: \(=12x^5-18x^4+30x^3-24x^2\)
d: \(=-3x^6+2.4x^5-1.2x^4+1.8x^2\)
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Thực hiện phép tínha,left(dfrac{1}{x^2+x}-dfrac{2-x}{x+1}right):left(dfrac{1}{x}+x-2right)b,left(dfrac{3x}{1-3x}+dfrac{2x}{3x+1}right):dfrac{6x^2+10x}{1-6x+9x^2}c,left(dfrac{9}{x^3-9x}+dfrac{1}{x+3}right):left(dfrac{x-3}{x^2+3x}-dfrac{x}{3x+9}right)d,dfrac{x+1}{x+2}:left(dfrac{x+2}{x+3}:dfrac{x+3}{x+1}right)e,dfrac{8}{left(x^2+3right)left(x^2-1right)}+dfrac{2}{x^2+3}+dfrac{1}{x+1}f,dfrac{x+y}{2left(x-yright)}-dfrac{x-y}{2left(x+yright)}+dfrac{2y^2}{x^2-y^2}g,dfrac{x-1}{x^3}-dfrac{x+1}{x^3-x^2}+d...
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Thực hiện phép tính
\(a,\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(b,\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
\(c,\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)
\(d,\dfrac{x+1}{x+2}:\left(\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\right)\)
\(e,\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}+\dfrac{2}{x^2+3}+\dfrac{1}{x+1}\)
\(f,\dfrac{x+y}{2\left(x-y\right)}-\dfrac{x-y}{2\left(x+y\right)}+\dfrac{2y^2}{x^2-y^2}\)
\(g,\dfrac{x-1}{x^3}-\dfrac{x+1}{x^3-x^2}+\dfrac{3}{x^3-2x^2+x}\)
\(h,\dfrac{x^3}{x-1}-\dfrac{x^2}{x+1}-\dfrac{1}{x-1}+\dfrac{1}{x+1}\)
a) Ta có: \(\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\left(\dfrac{1}{x\left(x+1\right)}+\dfrac{x+2}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\dfrac{x^2+2x+1}{x\left(x+1\right)}:\dfrac{x^2-2x+1}{x}\)
\(=\dfrac{\left(x+1\right)^2}{x\left(x+1\right)}\cdot\dfrac{x}{\left(x-1\right)^2}\)
\(=\dfrac{x+1}{\left(x-1\right)^2}\)
b) Ta có: \(\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
\(=\dfrac{3x\left(3x+1\right)+2x\left(1-3x\right)}{\left(1-3x\right)\left(1+3x\right)}:\dfrac{2x\left(3x+5\right)}{\left(1-3x\right)^2}\)
\(=\dfrac{9x^2+3x+2x-6x^2}{\left(1-3x\right)\left(1+3x\right)}:\dfrac{2x\left(3x+5\right)}{\left(1-3x\right)^2}\)
\(=\dfrac{3x^2+5x}{\left(1-3x\right)\left(1+3x\right)}\cdot\dfrac{\left(1-3x\right)^2}{2x\left(3x+5\right)}\)
\(=\dfrac{x\left(3x+5\right)}{1+3x}\cdot\dfrac{1-3x}{2x\left(3x+5\right)}\)
\(=\dfrac{2\left(1-3x\right)}{3x+1}\)
c) Ta có: \(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)
\(=\left(\dfrac{9}{x\left(x-3\right)\left(x+3\right)}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x\left(x+3\right)}-\dfrac{x}{3\left(x+3\right)}\right)\)
\(=\dfrac{9+x\left(x-3\right)}{x\left(x-3\right)\left(x+3\right)}:\dfrac{3\left(x-3\right)-x^2}{3x\left(x+3\right)}\)
\(=\dfrac{9+x^2-3x}{x\left(x-3\right)\left(x+3\right)}\cdot\dfrac{3x\left(x+3\right)}{3x-9-x^2}\)
\(=\dfrac{x^2-3x+9}{x-3}\cdot\dfrac{3}{-\left(x^2-3x+9\right)}\)
\(=\dfrac{-3}{x-3}\)
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1. Thực hiện phép tính:
a. \(3x^n\left(6x^{n-3}+1\right)-2x^n\left(9x^{n-3}-1\right)\)
b. \(5^{n+1}-4.5^n\)
c. \(6^2.6^4-4^3\left(3^6-1\right)\)
a:
=\(18x^{2n-3}+3x^n-18^{2n-3}+2x^n\)
\(=5x^n\)
b: \(=5^n\cdot5-4\cdot5^n=5^n\)
c: \(=6^6-4^3\cdot3^6+4^3\)
\(=2^6\cdot3^6-2^6\cdot3^6+64=64\)
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