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Bài làm:
a) \(M=90.10^n-10^{n+2}+10^{n+1}\)
\(M=9.10.10^n-10^{n+2}+10^{n+1}\)
\(M=10^{n+1}\left(9-10+1\right)\)
\(M=10^{n+1}.0=0\)
b) \(N=x\left(x+y\right)-y\left(x+y\right)\)
\(N=\left(x-y\right)\left(x+y\right)\)
\(N=x^2-y^2\)
c) \(P=y\left(x^{n-1}+y^{n-1}\right)-x^{n-1}\left(x+y\right)\)
\(P=x^{n-1}y+y^n-x^n-x^{n-1}y\)
\(P=y^n-x^n\)
Học tốt!!!!
1: \(2x^n+1\left(x^n-1-y^n-1\right)+y^n-1\left(2x^n+1-y^n+1\right)\)
\(=2x^n+x^n-1-y^n-1+y^n-2x^n-1+y^n-1\)
\(=x^n-y^n-4\)
2: \(\left(x^2-1\right)\left(x^2+2x\right)\)
\(=x^2\left(x^2+2x\right)-1\left(x^2+2x\right)\)
\(=x^4+2x^3-x^2-2x\)
4: \(4\left(x-6\right)-x^2\left(2+3x\right)+x\left(5x-4\right)+3x^2\left(x-1\right)\)
\(=4x-24-2x^2-3x^3+5x^2-4x+3x^3-3x^2\)
\(=-24\)
\(a,N=\dfrac{x^2+xy+y^2}{\left(x-y\right)\left(x+y\right)}\cdot\dfrac{\left(x-y\right)\left(x^4-y^4\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\\ N=\dfrac{\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)}{\left(x-y\right)\left(x+y\right)}=x^2+y^2\\ b,N=\left(x+y\right)^2-2xy=0-2\cdot1=-2\)
ĐKXĐ: \(x\ne y\)
a) \(N=\dfrac{x^2+y\left(x+y\right)}{\left(x-y\right)\left(x+y\right)}:\dfrac{\left(x-y\right)\left(x^2+xy+y^2\right)}{x^4\left(x-y\right)-y^4\left(x-y\right)}=\dfrac{x^2+xy+y^2}{\left(x-y\right)\left(x+y\right)}.\dfrac{\left(x-y\right)^2\left(x+y\right)\left(x^2+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}=x^2+y^2\)
b) \(x+y=0\Leftrightarrow\left(x+y\right)^2=0\Leftrightarrow x^2+y^2-2xy=0\)
\(\Leftrightarrow N=x^2+y^2=0+2xy=2.1=2\)
\(x\left(x^2-y\right)-x^2\left(x+y\right)+y\left(x^2-x\right)\)
\(=x^3-xy-x^3-x^2y+x^2y-xy=-2xy\)(1)
Thay \(x=\frac{1}{2};y=-100\) vào (1), ta có:
\(-2.\frac{1}{2}.-100=100\)
1)\(n^2\left(n-1\right)\left(n+1\right)-\left(n^2+2\right)\left(n^2-2\right)=n^2\left(n^2-1\right)-\left(n^4-4\right)=n^4-n^2-n^4+4\)
\(=-n^2+4\)
2)\(\left(y+3\right)\left(y-3\right)\left(y^2+9\right)-\left(y^2-4\right)\left(y^2+4\right)=\left(y^2-9\right)\left(y^2+9\right)-\left(y^4-16\right)\)
\(=y^4-81-y^4+16=-65\)
3)\(\left(x-2y+3\right)\left(x+2y-3\right)-\left(x-2y\right)\left(x+2y\right)=\left(x+3\right)^2-4y^2-\left(x^2-4y^2\right)\)
\(=x^2+6x+9-4y^2-x^2+4y^2=6x+9\)
4)\(\left(a+b+c\right)^2=a^2+b^2+c^2+2ab+2bc+2ac\)
5)\(\left(a+b-c\right)^2=a^2+b^2+c^2+2ab-2bc-2ac\)
6)\(\left(a-b-c\right)^2=a^2+b^2+c^2-2ab+2bc-2ac\)
Học tốt nha bạn !
