1. Thực hiện phép tính
a. \(\left(-2xy^2z^3\right)^3\). \(\left(\dfrac{5}{2}xy^3\right)^2\). \(\left(\dfrac{-4}{125}xy\right)\)
b. \(2^1_3x^2y^5-3^2_5x^3y-1^1_2x^2y^5+2^2_3x^3y\)
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a: =-4xyz^2
b: =-9x^2y
c: =16x^2y^2
d: =1/6x^2y^3
e: =13/6x^3y^2
f: =7/12x^4y
a) -xyz² - 3xz.yz
= -xyz² - 3xyz²
= -4xyz²
b) -8x²y - x.(xy)
= -8x²y - x²y
= -9x²y
c) 4xy².x - (-12x²y²)
= 4x²y² + 12x²y²
= 16x²y²
d) 1/2 x²y³ - 1/3 x²y.y²
= 1/2 x²y³ - 1/3 x²y³
= 1/6 x²y³
e) 3xy(x²y) - 5/6 x³y²
= 3x³y² - 5/6 x³y²
= 13/6 x³y²
f) 3/4 x⁴y - 1/6 xy.x³
= 3/4 x⁴y - 1/6 x⁴y
= 7/12 x⁴y
a: \(5x^2y^4:10x^2y=\dfrac{1}{2}y^3\)
c: \(\left(-xy\right)^{10}:\left(-xy\right)^5=-x^5y^5\)
a: \(=\dfrac{27a^6b^3\cdot a^2b^6}{a^8b^8}=27b\)
b: \(=3y^2-5x^2y^3-2y^2+3x^2y^3\)
\(=y^2-2x^2y^3\)
c: \(=6x-y+2x^2+3y-2x^2+x\)
\(=7x+2y\)
d: \(=x-y+2y^2-6xy+\dfrac{10x^2}{y}\)
a: \(=3y^2-5x^2y^3-2y^2+3x^2y^3=y^2-2x^2y^3\)
b: \(=6x-y+2x^2+3y^2-2x^2+x=7x-y+3y^2\)
c: \(=x-y+4y^2-6xy+\dfrac{10x^2}{y}\)
\(a.\left(9x^2y^3-15x^4y^4\right):3x^2y-\left(2-3x^2y\right)y^2\)
\(=3y^2-5x^2y^3-2y^2+3x^2y^3\)
\(=y^2-2x^2y^3\)
\(b.\left(6x^2-xy\right):x+\left(2x^3y+3xy^2\right):xy-\left(2x-1\right)x\)
\(=6x-y+2x^2+3y-2+x\)
\(=2x^2+7x+2y-2\)
\(c.\left(x^2-xy\right):x+\left(6x^2y^5-9x^3y^4+15x^4y^3\right):\dfrac{3}{2}x^2y^3\)
\(=x-y+4y^2-6xy+10x^2\)
\(ĐK:x\ne y;x\ne-y;x^2+xy+y^2\ne0;x^2-xy+y^2\ne0\)
\(A=\dfrac{x^2-xy+y^2}{x^2+xy+y^2}\cdot\left[1:\dfrac{\left(x^3+y^3\right)\left(x^2+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2+y^2\right)}\right]\\ A=\dfrac{x^2-xy+y^2}{x^2+xy+y^2}\cdot\dfrac{\left(x-y\right)\left(x+y\right)\left(x^2+xy+y^2\right)\left(x^2+y^2\right)}{\left(x+y\right)\left(x^2-xy+y^2\right)\left(x^2+y^2\right)}\\ A=x-y=B\)
\(x=0;y=0\Leftrightarrow B=0\)
Giá trị của A không xác định vì \(x=y\) trái với ĐK:\(x\ne y\)
Vậy \(A\ne B\)
a: \(=\dfrac{5}{3}x^2-x+\dfrac{1}{3}\)
b: \(=-5y-9+xy\)
a, \(\left(-2xy^2z^3\right)^3.\left(\dfrac{5}{2}xy^3\right)^2.\left(\dfrac{-4}{125}xy\right)\)
\(=\left(-2\right)^3.x^3.\left(y^2\right)^3.z^3.\left(\dfrac{5}{2}\right)^2.x^2.\left(y^3\right)^2.\dfrac{-4}{125}.x.y\)
\(=\left(-2\right)^3.\left(\dfrac{5}{2}\right)^2.\dfrac{-4}{125}.\left(x^3.x^2.x\right).\left(y^6.y^6.y\right).z^3\)
\(=\left(-8\right).\dfrac{25}{4}.\dfrac{-4}{125}.x^6.y^{13}.z^3\)
\(=1,6.x^6.y^{13}.z^3\)
a, \(\left(-2xy^2z^3\right).\left(\dfrac{5}{2}xy^3\right)^2.\left(\dfrac{-4}{125}xy\right)\)
= \(\left(-5x^2y^5z^3\right)^5.\left(\dfrac{-4}{125}xy\right)\)
= \(\left(\dfrac{4}{25}x^3y^6z^3\right)^5\)
b, \(2\dfrac{1}{3}x^2y^5-3\dfrac{2}{5}x^3y-1\dfrac{1}{2}x^2y^5+2\dfrac{2}{3}x^3y\)
= \(\dfrac{7}{3}x^2y^5-\dfrac{17}{5}x^3y-\dfrac{3}{2}x^2y^5+\dfrac{8}{3}x^3y\)
= \(\dfrac{5}{6}x^2y^5-\dfrac{11}{15}x^3y\)