\(\left(a-1\right)^3-\left(a+1\right)^3=a^3-3a^2+3a-1-a^3-3a^2-3a-1=-6a^2-2=-2\left(3a^2+1\right)\)

\(\left(a-1\right)^3-\left(a+1\right)^3\)

\(=\left[\left(a-1\right)-\left(a+1\right)\right]\left[\left(a-1\right)^2+\left(a-1\right)\left(a+1\right)+\left(a+1\right)^2\right]\)

\(=\left(-2\right)\left(a^2-2a+1+a^2-1+a^2+2a+1\right)\)

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

\(a^6-b^6=\left(a^3\right)^2-\left(b^3\right)^2=\left(a^3-b^3\right)\left(a^3+b^3\right)=\left(a-b\right)\left(a^2+ab+b^2\right).\left(a+b\right)\left(a^2-ab+b^2\right)\)

\(a,\left(-64\right)+\left(x-3\right)^3\)

\(=\left(-4\right)^3+\left(x-3\right)^3\)

\(=\left(-4+x-3\right)\left[\left(-4\right)^2-\left(-4\right)\left(x-3\right)+\left(x-3\right)^2\right]\)

\(a,-64+\left(x-3\right)^3\)

\(=\left(-4\right)^3+\left(x-3\right)^3\)

\(=\left(-4+x-3\right)\left[\left(-4\right)^2-\left(-4\right)\left(x-3\right)+\left(x-3\right)^2\right]\)

\(=\left(x-7\right)\left(16+4x-12+x^2-6x+9\right)\)

\(=\left(x-7\right)\left(x^2-2x+13\right)\)

Bài 1 :

a) (2x + 1)³ = 125

=> (2x + 1)³ = 5³

=> 2x + 1 = 5

=> 2x = 5 - 1

=> 2x = 4

=> x = 2

b) (x - 5)⁴ = (x - 5)⁶

Với hai mũ khác nhau , ta chỉ có thể tìm được giá trị biểu thức bằng 1 hoặc 0 (giá trị của chúng bằng nhau)

+) (x - 5)⁴ = (x - 5)⁶ = 0

=> (x - 5)⁴ = 0

=> (x - 5)⁴ = 0⁴

=> x - 5 = 0 => x = 0 + 5 = 5

+) (x - 5)⁴ = (x- 5)⁶ = 1

=> (x - 5)⁴ = 1

=> (x - 5)⁴ = 1⁴

=> x - 5 = 1

=> x = 1 + 5

=> x = 6

Bài 4 :

a³ . a⁹ = a^{3 + 9} = a¹²

(a⁵)⁷.(a⁶)⁴ .a¹² = a³⁵ . a²⁴ . a¹² = a^{35 + 24 + 12} = a⁷¹

4.5² - 2.3² = 4.25 - 2.9

= 100 - 18

= 82

mong cac ban giup, minh can gap lam,tuy minh trinh bay hoi xau nhung mong cac ban giup

3.viet cac tich, thuong sau duoi dang luy thua:

a) \(\dfrac{2^{10}}{8^3}\)

\(=\dfrac{2^{10}}{\left(2^3\right)^3}\)

\(=\dfrac{2^{10}}{2^9}\)

\(=2^1\)