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 the expression (6x - 2)^2 * (0.5x)^4, we first need to expand the terms inside the parentheses:
(6x - 2)^2 = (6x - 2)(6x - 2)
= 36x^2 - 12x - 12x + 4
= 36x^2 - 24x + 4
(0.5x)^4 = (0.5)^4 * x^4
= (1/16) * x^4
= x^4 / 16
Now, substitute these expanded forms back into the original expression:
(36x^2 - 24x + 4)(x^4 / 16)
Next, distribute the x^4/16 to each term inside the parentheses:
36x^2 * (x^4 / 16) - 24x * (x^4 / 16) + 4 * (x^4 / 16)
= 36x^6 / 16 - 24x^5 / 16 + 4x^4 / 16
= (36/16)x^6 - (24/16)x^5 + (4/16)x^4
= 9/4 * x^6 - 3/2 * x^5 + 1/4 * x^4
Therefore, the simplified expression is 9/4x^6 - 3/2x^5 + 1/4x^4.
can you shorten this a little while keeping the answer correct
To simplify the expression (6x - 2)^2 * (0.5x)^4:
(6x - 2)^2 = 36x^2 - 24x + 4
(0.5x)^4 = x^4 / 16
(36x^2 - 24x + 4)(x^4 / 16) = 9/4x^6 - 3/2x^5 + 1/4x^4
Therefore, the simplified expression is 9/4x^6 - 3/2x^5 + 1/4x^4.