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Ta có:
90.10k - 10k+2 + 10k+1
= 9.10.10k - 10k+2 + 10k+1
= (10 - 1).10k+1 - 10k+2 + 10k+1
= 10k+2 - 10k+1 - 10k+2 + 10k+1
= 0
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) \(\left(x^2-5\right)\left(x+3\right)+\left(x+4\right)\left(x-x^2\right)\)
\(=\left(x+3\right).x^2-5\left(x+3\right)+\left(x+4\right)\left(x-1x^2\right)\)
\(=x^3+3x^2-5x-15+\left(x+4\right)\left(x-x^2\right)\)
\(=x^3+3x^2-5x-15-x^3+x^2-4x^2+4x\)
\(=3x^2-5x-15-3x^2+4x\)
\(=-x-15\)
90.10k-10k+2+10k+1
=9.10.10k-10k+1.10+10k+1
=10k+1.(9-10+1)
=10k+1.0
=0
\(90.10^k-10^{k+2}+10^{k+1}\)
\(=10^k\left(90-10^2+10\right)\)
\(=10^k.0=0\)