To evaluate the expression [tex]\(4(5x - 3 - 2x)^2\)[/tex] where [tex]\(x = 5\)[/tex], follow these detailed steps:
1. Substitute the value of [tex]\(x\)[/tex]:
Substitute [tex]\(x = 5\)[/tex] into the expression.
[tex]\[
4(5(5) - 3 - 2(5))^2
\][/tex]
2. Evaluate the terms inside the parentheses:
First, calculate [tex]\(5x\)[/tex] and [tex]\(2x\)[/tex]:
[tex]\[
5 \cdot 5 = 25
\][/tex]
[tex]\[
2 \cdot 5 = 10
\][/tex]
Now, substitute these values back into the expression:
[tex]\[
4(25 - 3 - 10)^2
\][/tex]
3. Simplify the inner expression:
Perform the subtraction inside the parentheses:
[tex]\[
25 - 3 = 22
\][/tex]
[tex]\[
22 - 10 = 12
\][/tex]
So now the expression is:
[tex]\[
4(12)^2
\][/tex]
4. Square the inner result:
Calculate [tex]\(12^2\)[/tex]:
[tex]\[
12^2 = 144
\][/tex]
5. Multiply by 4:
Finally, multiply the squared result by 4:
[tex]\[
4 \cdot 144 = 576
\][/tex]
Thus, the evaluated result of the expression [tex]\(4(5x - 3 - 2x)^2\)[/tex] when [tex]\(x = 5\)[/tex] is [tex]\(\boxed{576}\)[/tex].
