rút gọn biểu thức :
a,27(1-x)(x^2+x+1)+81x(x-1)
b,y[x^2+x(x-y)+(x-y)^2]+(x-y)^3
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2 tháng 10 2018
Bài 1:
a.\(\left(x+y\right)^2-\left(x-y\right)^2=\left(x+y-x+y\right)\left(x+y+x-y\right)=2\left(x+y\right)\)
b.\(2\left(x+y\right)\left(x-y\right)+\left(x+y\right)^2+\left(x-y\right)^2=\left(x+y+x-y\right)^2=4x^2\)
12 tháng 7 2021
a) Ta có: \(\dfrac{x^2}{y^2}:\sqrt{\dfrac{x^2}{y^4}}\)
\(=\dfrac{x^2}{y^2}:\dfrac{x}{y^2}\)
=x
b) Ta có: \(\sqrt{\dfrac{27\left(x-1\right)^2}{12}}+\dfrac{3}{2}-\left(x-2\right)\sqrt{\dfrac{50x^2}{8\left(x-2\right)^2}}\)
\(=\sqrt{\dfrac{9}{4}}\cdot\sqrt{\left(x-1\right)^2}+\dfrac{3}{2}-\left(x-2\right)\cdot\sqrt{\dfrac{25}{4}}\cdot\sqrt{\dfrac{x^2}{\left(x-2\right)^2}}\)
\(=\dfrac{3}{2}\cdot\left(x-1\right)+\dfrac{3}{2}-\left(x-2\right)\cdot\dfrac{5}{2}\cdot\dfrac{x}{2-x}\)
\(=\dfrac{3}{2}x-\dfrac{3}{2}+\dfrac{3}{2}-\dfrac{5}{2}\left(x-2\right)\cdot\dfrac{-x}{x-2}\)
\(=\dfrac{3}{2}x+\dfrac{5}{2}\cdot\left(x\right)\)
=4x
1 tháng 7 2021
a) Ta có: \(\left(3x-2\right)^2+2\left(3x-2\right)\left(3x+2\right)+\left(3x+2\right)^2\)
\(=\left(3x-2+3x+2\right)^2\)
\(=36x^2\)(1)
Thay \(x=-\dfrac{1}{3}\) vào biểu thức (1), ta được:
\(36\cdot\left(-\dfrac{1}{3}\right)^2=36\cdot\dfrac{1}{9}=4\)
b) Sửa đề: \(\left(x+y-7\right)^2-2\cdot\left(x+y-7\right)\left(y-6\right)+\left(y-6\right)^2\)
Ta có: \(\left(x+y-7\right)^2-2\cdot\left(x+y-7\right)\left(y-6\right)+\left(y-6\right)^2\)
\(=\left(x+y-7-y+6\right)^2\)
\(=\left(x-1\right)^2=100^2=10000\)
12 tháng 11 2021
5: \(=\dfrac{1}{x-y}\cdot x^3\cdot\left(x-y\right)^2=x^3\left(x-y\right)\)
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a) \(27\left(1-x\right)\left(x^2+x+1\right)+81x\left(x-1\right)\)
\(=27\left(1-x^3\right)+81\left(x^2-x\right)\)
\(=27-27x^3+81x^2-81x\)
b) \(y\left[x^2+x\left(x-y\right)+\left(x-y\right)^2\right]+\left(x-y\right)^3\)
\(=y\left[x^2+x^2-xy+x^2-2xy+y^2\right]+x^3-3x^2y+3xy^2-y^3\)
\(=y\left(3x^2-3xy+y^2\right)+x^3-3x^2y+3xy^2-y^3\)
\(=3x^2y-3xy^2+y^3+x^3-3x^2y+3xy^2-y^3=x^3\)
a, \(27\left(1-x\right)\left(x^2+x+1\right)+81x\left(x-1\right)=27-27x^3+81x^2-81x\)
b, \(y\left[x^2+x\left(x-y\right)+\left(x-y\right)^2\right]+\left(x-y\right)^3\)
\(=3x^2y-3xy^2+y^3+x^3-3x^2y+3xy^2-y^3=x^3\)