Question 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 can first expand the first binomial and then raise the second binomial to the fourth power.
Expanding (6x - 2)^2:
(6x - 2)^2 = (6x - 2)(6x - 2)
= 36x^2 - 12x - 12x + 4
= 36x^2 - 24x + 4
Next, raising (0.5x)^4:
(0.5x)^4 = (0.5)^4 * (x^4)
= 0.0625 * x^4
= 0.0625x^4
Now, we can multiply the two simplified expressions:
(36x^2 - 24x + 4) * (0.0625x^4)
Multiplying each term of the first expression by the second expression:
= 36x^2 * 0.0625x^4 - 24x * 0.0625x^4 + 4 * 0.0625x^4
= 2.25x^6 - 1.5x^5 + 0.25x^4
Therefore, (6x - 2)^2(0.5x)^4 simplifies to 2.25x^6 - 1.5x^5 + 0.25x^4.