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Simplify (6x−2)2(0.5x)4
. Show your work.
(2 points)
To simplify the expression (6x−2)2(0.5x)4, begin by simplifying the exponents:
(6x-2)² = (6x-2)(6x-2) = 36x² - 24x + 4
(0.5x)⁴ = (0.5)⁴ * (x)⁴ = 0.0625x⁴
Now, multiply the simplified expressions:
(36x² - 24x + 4)(0.0625x⁴)
= 0.0625x⁴ * 36x² - 0.0625x⁴ * 24x + 0.0625x⁴ * 4
= 2.25x⁶ - 1.5x⁵ + 0.25x⁴
Therefore, the simplified expression is 2.25x⁶ - 1.5x⁵ + 0.25x⁴.