Sure, let's find the value of the expression [tex]\(\frac{(5x + x)^2(6 - x)}{x}\)[/tex] when [tex]\(x = 2\)[/tex].
First, let's rewrite the expression for clarity:
[tex]\[
\frac{(5x + x)^2(6 - x)}{x}
\][/tex]
We can simplify the inner part of the numerator step-by-step:
1. Combine like terms inside the parentheses:
[tex]\[
5x + x = 6x
\][/tex]
2. Substitute [tex]\(x = 2\)[/tex] into the expression [tex]\(6x\)[/tex]:
[tex]\[
6 \times 2 = 12
\][/tex]
3. Square the result:
[tex]\[
12^2 = 144
\][/tex]
Next, we incorporate the remaining part of the expression:
4. Substitute [tex]\(x = 2\)[/tex] into [tex]\(6 - x\)[/tex]:
[tex]\[
6 - 2 = 4
\][/tex]
5. Multiply the squared result by [tex]\(6 - x\)[/tex]:
[tex]\[
144 \times 4 = 576
\][/tex]
Now, we divide by the denominator:
6. Substitute [tex]\(x = 2\)[/tex] into the denominator [tex]\(x\)[/tex]:
[tex]\[
2
\][/tex]
7. Divide the previous result by the denominator:
[tex]\[
\frac{576}{2} = 288.0
\][/tex]
So, the value of the expression [tex]\(\frac{(5x + x)^2(6 - x)}{x}\)[/tex] when [tex]\(x = 2\)[/tex] is [tex]\(288.0\)[/tex].
