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a) \(\left(\dfrac{1}{3}x^2y\right).\left(15xy^3\right)=5x^3y^4\)
b) \(\left(\dfrac{3}{5}x^3y\right).\left(-2x^3y^5\right)=-\dfrac{6}{5}x^6y^6\)
c) \(\left(-\dfrac{1}{2}x^2y\right).\left(2xy^3\right).\left(-\dfrac{5}{8}x^3y^3\right)=\dfrac{5}{8}x^6y^7\)
![](https://rs.olm.vn/images/avt/0.png?1311)
x2y + 2x2y + 3x2y + 4x2y + .... + nx2y = 55x2y
\(\Rightarrow x^2y\left(1+2+...+n\right)=55x^2y\)
\(\Rightarrow1+2+...+n=55\)
\(\Rightarrow\dfrac{\left(\dfrac{n-1}{1}+1\right).\left(n+1\right)}{2}=55\)
\(\Rightarrow n\left(n+1\right)=55.2=110\)
\(\Rightarrow n^2+n-110=0\)
\(\Rightarrow n^2-10n+11n-110=0\)
\(\Rightarrow n\left(n-10\right)+11\left(n-10\right)=0\)
\(\Rightarrow\left(n-10\right)\left(n+11\right)=0\)
\(\Rightarrow n-10=0\) hay \(n+11=0\)
\(\Rightarrow n=10\left(nhận\right)\) hay \(n=-11\left(loại\right)\)
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a)M=3x2y-2xy2+2x2y+2xy+3xy2
=\(5x^2y+xy^2+2xy\)
N=2x2y+xy+xy2-4xy2-5xy
=\(2x^2y-3xy^2-4xy\)
b) M-N=(\(5x^2y+xy^2+2xy\))-(\(2x^2y-3xy^2-4xy\))
=\(5x^2y+xy^2+2xy\)\(-\)\(2x^2y+3xy^2+4xy\)
=\(3x^2y+4xy^2+6xy\)
M+N=\(5x^2y+xy^2+2xy\)\(+\)\(2x^2y-3xy^2-4xy\)
=\(7x^2y-2xy^2-2xy\)
c) Ta có P(x)=0
\(\Rightarrow\)6-2x=0
\(\Rightarrow\)x=3
Vậy x=3 là nghiệm của đa thức P(x)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có
A − B = 3 x 3 y 2 + 2 x 2 y − x y − 4 x y − 3 x 2 y + 2 x 3 y 2 + y 2 = 3 x 3 y 2 + 2 x 2 y − x y − 4 x y + 3 x 2 y − 2 x 3 y 2 − y 2 = 3 x 3 y 2 − 2 x 3 y 2 + 2 x 2 y + 3 x 2 y + ( − x y − 4 x y ) − y 2 = x 3 y 2 + 5 x 2 y − 5 x y − y 2
Chọn đáp án C
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có
A + B = 3 x 3 y 2 + 2 x 2 y − x y + 4 x y − 3 x 2 y + 2 x 3 y 2 + y 2 = 3 x 3 y 2 + 2 x 3 y 2 + 2 x 2 y − 3 x 2 y + ( − x y + 4 x y ) + y 2 = 5 x 3 y 2 − x 2 y + 3 x y + y 2
Chọn đáp án D
![](https://rs.olm.vn/images/avt/0.png?1311)
M-N-P=4x3-2x2y+xy+1-3x2y-2xy+5-4x3+5x2y-3xy-1
=-4xy+5
p-n-m=4x3-5x2y+3x2y+1-3x2y-2xy+5-4x3+2x2y-xy-1
=-6x2y+5
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