The expanded algebraic expression is x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64
How to expand the algebraic expression
From the question, we have the following parameters that can be used in our computation:
(x - 2)⁶
This is a binomial expression that can be expanded using Pascal triangle
The power of the expression is 6
At n = 6, we have the following coefficients
1 6 16 20 16 6 1
So, we have
(x - 2)⁶ = 1 * x⁶ + 6 * x⁵ * (-2) + 16 * x⁴ * (-2)² + 20 * x³ * (-2)³ + 16 * x² * (-2)⁴ + 6 * x * (-2)⁵ + 1 * (-2)⁶
Expand the exponents
(x - 2)⁶ = x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64
Hence, the expanded algebraic expression is x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64