Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify (6x−2)2(0.5x)4 . Show your work
To simplify (6x - 2)²(0.5x)⁴, we need to first expand the quadratic term (6x - 2)² and then multiply it with (0.5x)⁴.
Expanding (6x - 2)²:
(6x - 2)² = (6x - 2)(6x - 2)
= (6x)(6x) + (6x)(-2) + (-2)(6x) + (-2)(-2)
= 36x² - 12x - 12x + 4
= 36x² - 24x + 4
Multiplying with (0.5x)⁴:
(36x² - 24x + 4)(0.5x)⁴
= 36x² * (0.5x)⁴ - 24x * (0.5x)⁴ + 4 * (0.5x)⁴
= 36 * 0.5⁴ * x² * x⁴ - 24 * 0.5⁴ * x * x⁴ + 4 * 0.5⁴ * x⁴
= 36 * 0.0625 * x⁶ - 24 * 0.0625 * x⁵ + 4 * 0.0625 * x⁴
= 2.25x⁶ - 1.5x⁵ + 0.25x⁴
Therefore, the simplified form of (6x - 2)²(0.5x)⁴ is 2.25x⁶ - 1.5x⁵ + 0.25x⁴.