Simplify (6x−2)2(0.5x)4 . Show your work.

Answer 1

To simplify the expression (6x - 2)^2(0.5x)^4, we can simplify each term separately and then multiply them together.

First, simplify (6x - 2)^2:

(6x - 2)^2 = (6x - 2)(6x - 2)
= 36x^2 - 12x - 12x + 4
= 36x^2 - 24x + 4

Next, simplify (0.5x)^4:

(0.5x)^4 = (0.5^4)(x^4)
= 0.0625x^4

Finally, multiply the two simplified terms together:

(36x^2 - 24x + 4)(0.0625x^4)
= 0.0625x^4(36x^2 - 24x + 4)
= 0.0625(36x^6 - 24x^5 + 4x^4)
= 2.25x^6 - 1.5x^5 + 0.25x^4

Therefore, the simplified expression is 2.25x^6 - 1.5x^5 + 0.25x^4.