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Simplify (6x−2)2(0.5x)4
. Show your work.
First, we can simplify each term in the expression:
(6x - 2)^2 can be expanded as (6x - 2)(6x - 2) which gives us 36x^2 - 24x + 4.
(0.5x)^4 can be expanded as (0.5x)(0.5x)(0.5x)(0.5x) which gives us 0.0625x^4.
Now, we can multiply the two simplified terms together:
(36x^2 - 24x + 4)(0.0625x^4)
To multiply these two expressions, we distribute each term in the first expression to each term in the second expression:
(36x^2)(0.0625x^4) - (24x)(0.0625x^4) + (4)(0.0625x^4)
Simplifying each term:
2.25x^6 - 1.5x^5 + 0.25x^4
Therefore, the simplified expression is 2.25x^6 - 1.5x^5 + 0.25x^4.