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What is the value of [tex]\frac{(5x + x)^2 (6 - x)}{x}[/tex] when [tex]x = 2[/tex]?

Sagot :

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].