Question

Tính:

a. 3xⁿ(6x^n-3 + 1) - 2xⁿ(9x^n-3 -1)

b. 5ⁿ⁺¹ - 4.5ⁿ

c. 6².6⁴-4³(3⁶-1)

Answer 1

\(a,3x^n\left(6x^{n-3}+1\right)-2x^n\left(9x^{n-3}-1\right)\)

\(=x^n\left[3\left(6x^{n-3}+1\right)-2\left(9x^{n-3}-1\right)\right]\)

\(=x^n\left(18x^{n-3}+3-18x^{n-3}+2\right)\)

\(=5x^n\)

\(b,5^{n+1}-4.5^n\)\(=5^n.5+5^n.4=5^n\left(5+4\right)=45^n\)

\(c,6^2.6^4-4^3\left(3^6-1\right)\)

\(=6^6-4^3.3^6+4^3\)

\(=2^6.3^6-4^3.3^6+4^3\)

\(=3^6\left(2^6-4^3\right)+4^3\)

\(=3^6\left[\left(2^2\right)^3-4^3\right]+4^3=3^6.0+4^3=4^3=64\)