rút gọn đa 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)
giúp mk với nhé
Bài 1:Rút gọn các biểu thức:
a, 10n+1 -6.10n
b,2n+3 +2n+2 -2n+1 + 2n
c,90.10k - 10k+2 +10k+1
d,2,5.5n-3 x 10 +5n - 6.5n-1
\(d,2,5.5^{n-3}.2.5+5^n-6.5^{n-1}=5.5.5^{n-3}+5^n-6.5^{n-1}=5^2.5^{n-3}+5^n-6.5^{n-1}\)
\(=5^{n-3+2}+5^n-6.5^{n-1}=5^{n-1}\left(1+5-6\right)=5^{n-1}.0=0\)
a, \(10^{n+1}-6.10^n=10^n\left(10-6\right)=4.10^n\)
b. \(2^{n+3}+2^{n+2}-2^{n+1}+2^n=2^n\left(2^3+2^2-2+1\right)=2^n\left(8+4-2+1\right)=11.2^n\)
Mình cho bạn tự làm câu d mà không làm thôi làm cho vậy
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+\(^{5^n}\)-\(^{6.5^{n-1}}\)
a) \(10^{n+1}-6.10^n\)
\(=10^n.10-6.19^n\)
\(=10^n.\left(10-6\right)\)
\(=10^n.4\)
b) \(2^{n+3}+2^{n+2}-2^{n+1}+2^n\)
\(=2^n.2^3+2^n.2^2-2^n.2+2^n.1\)
\(=2^n.\left(2^3+2^2-2+1\right)\)
\(=2^n.11\)
c) \(90.10^k-10^{k+2}+10^{k+1}\)
\(=90.10^k-10^k.10^2+10^k.10\)
\(=10^k.\left(90-10^2+10\right)\)
\(=0\)
d) \(2,5.5^{n-3}.10+5^n-6.5^{n-1}\)
\(=\dfrac{2,5.5^n.10}{5^3}+5^n-\dfrac{6.5^n}{5}\)
\(=\dfrac{5^n}{5}+5^n-\dfrac{6.5^n}{5}\)
\(=\dfrac{5^n+5^{n+1}-6.5^n}{5}=\dfrac{5^n+5^n.5-6.5^n}{5}=\dfrac{5^n\left(1+5-6\right)}{5}=\dfrac{0}{5}=0\)
Rút gọn các biểu thức sau :
10n+1- 6.10n
2n+3+2n+2-2n+1+2n
90.102-10k+2+10k+1
25.5n-3.10+5n-6.5n-1
a) 10n + 1 - 6.10n
= 10n . 10 - 6 . 10n
= 10n . (10 - 6)
= 10n . 4
b) 2n + 3 + 2n + 2 - 2n + 1 + 2n
= 2n . 23 + 2n . 22 - 2n . 2 + 2n . 1
= 2n . (8 + 4 - 2 + 1)
= 2n . 11
Rút gọn
a) 10n+1 - 6 . 10
b) 2n+3 + 2n+2 - 2n+1 + 2n
c) 90 . 10k - 10k+2 + 10k+1
Rút gọn các biểu thức:
a, 10n+1
b, 2n+3 + 2n+1 - 2n+1 + 2n.
c, 90.10k - 10k+2 + 10k+1.
d, 2,5.5n-3 - 10.5n - 6.5n-1.
a: \(10^{n+1}=10^n\cdot10\)
b: \(2^{n+3}+2^{n+1}-2^{n+1}+2^n\)
\(=2^n\cdot8+2^n=9\cdot2^n\)
c: \(90\cdot10^k-10^{k+2}+10^{k+1}\)
\(=90\cdot10^k+10^k\cdot10-10^k\cdot100=0\)
Rút gọn các biểu thức:
a) \(90.10^k-10^{k+2}+10^{k+1}\)
b) \(2,5.5^{n-3}.10+5^n-6.5^{n-1}\)
a) Ta có:
\(90.10^k-10^{k+2}+10^{k+1}\)
\(=90.10^k-10^k.10^2+10^k.10\)
\(=10^k\left(90-10^2+10\right)\)
\(=10^k.0=0\)
b) Ta có:
\(2,5.5^{n-3}.10+5^n-6.5^{n-1}\)
\(=2,5.10.5^{n-3}+5^n-6.5^{n-1}\)
\(=5.5.5^{n-3}+5^n-6.5^{n-1}\)
\(=5^2.5^{n-3}+5^n-6.5^{n-1}\)
\(=5^{n-3+2}+5^n-6.5^{n-1}\)
\(=5^{n-1}\left(1+5-6\right)\)
\(=5^{n-1}.0=0\)
a) Rút gọn biểu thức:
\(90\times10^k-10^{k+2}+10^{k+1}=90\times10^k-10^k\times10^2+10^k\times10\) \(=10^k\times\left(90-10^2+10\right)\) \(=10^k\times\left(90-100+10\right)\) \(=10^k\times0=0\)
b) Rút gọn biểu thức:
\(2,5\times5^{n-3}\times10+5^n-6\times5^{n-1}=2,5\times\dfrac{5^n}{5^3}\times10+5^n-6\times\dfrac{5^n}{5}\) \(=2,5\times\dfrac{5^n}{125}\times10+5^n-\dfrac{6}{5}\times5^n\) \(=0,2\times5^n+5^n-1,2\times5^n\) \(=5^n\times\left(0,2+1-1,2\right)=5^n\times0=0\)
a/ 10n+1 - 6.10n
B/ 2n+3 + 2n+2 - 2n+1 +2n
C/ 90.10k - 10k +2 + 10k +1
D/ 2,5 . 5n-3 . 10+5n -6 .5n-1
\(a, 10^{n+1} -6.10 ^n\)
= \(10^n (10-6)=4.10^n\)
\(B/ 2^{n+3} + 2^{n+2} - 2^{n+1} +2^n\)
= \(2^n (2^3+2^2-2+1)\)
= \(2^n (8+4-2+1)\)
\(= 11.2^n\)
\(C/ 90.10^k - 10^{k +2} + 10^{k +1} \)
\(= 10^k(90-2+1)\)
= \(89.10^k\)
\(D/ 2,5 . 5^{n-3} . 10+5^n -6 .5^{n-1}\)
\(= 5.5.5^{n-3} +5^n-6.5^{n-1}\)
= \(5^2 .5^{n-3}+5^n-6.5^{n-1} \)
= \(5^{n-3+2}+5^n -6.5^{n-1}\)
\(= 5^{n-1}(1+5-6)\)
= \(5^{n-1}.0\)
= 0
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!
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. \(M+\left(6x^2-4xy\right)=7x^2-8xy+y^2\)
\(M=\left(7x^2-8xy+y^2\right)-\left(6x^2-4xy\right)\)
\(M=7x^2-8xy+y^2-6x^2+4xy\)
\(M=7x^2-6x^2-8xy+4xy+y^2\)
\(M=x^2-4xy+y^2\)
1a) 10n + 1 - 6.10n = 10n.10 - 6.10n = 10n.(10 - 6) = 10n.4
b) 2n + 3 + 2n + 2 - 2n + 1 + 2n = 2n.8 + 2n.4 - 2n.2 + 2n = 2n.(8 + 4 - 2 + 1) = 2n.11
c) 90.10k - 10k + 2 + 10k + 1 = 90.10k - 10k.100 + 10k.10 = (90 - 100 + 10).10k = 20.10k
d) 2,5.5n - 3.10 + 5n - 6.5n - 1 = 2,5.5n : 125.10 + 5n - 6.5n: 5 = 0,2.5n + 5n - 1,2.5n = (0,2 + 1 - 1,2).5n = 0
Bài1 : tìm x
b, \(x^2.\left(x^2+4\right)-x^2-4=0\)
\(a,\left(2x-1\right)^2-\left(4x^2-1\right)=0\)
bài 2 rút gọn
a, \(90.10^k-10^{k+2}+10^{k+1}\)
b,\(2,5.5^{n-3}.10+5^n-6.5^{n-1}\)
b) \(x^2\left(x^2+4\right)-x^2-4=0\)
.\(\Leftrightarrow x\left(x^2+4\right)-\left(x^2+4\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2+4\right)=0\)
\(\Rightarrow x-1=0\)(vì \(x^2+4>0\))
\(\Leftrightarrow x=1\)
Ta có : (2x - 1)2 - (4x2 - 1) = 0
<=> (2x - 1)2 - [(2x)2 - 12] = 0
<=> (2x - 1)2 - (2x - 1)(2x + 1) = 0
<=> (2x - 1)[2x - 1 - (2x + 1)] = 0
<=> (2x - 1)(-2) = 0
=> 2x - 1 = 0
=> 2x = 1
=> x = \(\frac{1}{2}\)
Vậy x = \(\frac{1}{2}\)