Question

1. Rút gọn các biểu thức:

a) \(10^{n+1}-6.10^n;\)

b) \(2^{n+3}+2^{n+2}-2^{n+1}+2^n;\)

c) \(90.10^k-10^{k+2}+10^{k+1};\)

d) \(2,5.5^{n-3}.10+5^n-6.5^{n-1}\)

2. Xác định đa thức M biết rằng: \(M+\left(6x^2-4xy\right)=7x^2-8xy+y^2\)

Mọi người giúp mình với ạ, mai mình học rồi. Cảm ơn mọi người nhiều lắm ạ!

Answer 1

1a) \(10^{n+1}-6\cdot10^n\)

\(=10^n\cdot10-6\cdot10^n\)

= \(10^n\left(10-6\right)\)

\(=10^n\cdot4\)

b) \(2^{n+3}+2^{n+2}-2^{n+1}+2^n\)

\(=2^n\cdot2^3+2^n\cdot2^2-2^n\cdot2+2^n\)

\(=2^n\left(2^3+2^2-2+1\right)\)

\(=2^n\cdot11\)

c) \(90\cdot10^k-10^{k+2}+10^{k+1}\)

\(=90\cdot10^k-10^k\cdot10^2+10^k\cdot10\)

\(=10^k\left(90-10^2+10\right)=0\)

d) \(2,5\cdot5^{n-3}\cdot10+5^n-6\cdot5^{n-1}\)

\(=\dfrac{2,5\cdot10\cdot5^n}{5^3}+5^n-\dfrac{6\cdot5^n}{5}\)

\(=\dfrac{5^n}{5}+5^n-\dfrac{6\cdot5^n}{5}\)

\(=\dfrac{5^n+5^n\cdot5-6\cdot5^n}{5}=\dfrac{5^n\left(5-6\right)+5^n}{5}=0\)

2. \(M+\left(6x^2-4xy\right)=7x^2-8xy+y^2\)

\(M=\left(7x^2-8xy+y^2\right)-\left(6x^2-4xy\right)\)

\(M=7x^2-8xy+y^2-6x^2+4xy\)

\(M=7x^2-6x^2-8xy+4xy+y^2\)

\(M=x^2-4xy+y^2\)

Answer 2

1a) 10^{n + 1} - 6.10ⁿ = 10ⁿ.10 - 6.10ⁿ = 10ⁿ.(10 - 6) = 10ⁿ.4

b) 2^{n + 3} + 2^{n + 2} - 2^{n + 1} + 2ⁿ = 2ⁿ.8 + 2ⁿ.4 - 2ⁿ.2 + 2ⁿ = 2ⁿ.(8 + 4 - 2 + 1) = 2ⁿ.11

c) 90.10^k - 10^{k + 2} + 10^{k + 1} = 90.10^k - 10^k.100 + 10^k.10 = (90 - 100 + 10).10^k = 20.10^k

d) 2,5.5^{n - 3}.10 + 5ⁿ - 6.5^{n - 1} = 2,5.5ⁿ : 125.10 + 5ⁿ - 6.5ⁿ: 5 = 0,2.5ⁿ + 5ⁿ - 1,2.5ⁿ = (0,2 + 1 - 1,2).5ⁿ = 0