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Evaluate the expression [tex][tex]$4p^2 + 7q^3$[/tex][/tex] if [tex]$p = -3$[/tex] and [tex]$q = -2$[/tex].

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GinnyAnsweridn
Sure, let's break down the solution for the given expression [tex]\(4p^2 + 7q^3\)[/tex] where [tex]\(p = -3\)[/tex] and [tex]\(q = -2\)[/tex].

Step 1: Calculate [tex]\(4p^2\)[/tex]

First, substitute [tex]\(p = -3\)[/tex] into the expression [tex]\(4p^2\)[/tex]:

[tex]\[4p^2 = 4(-3)^2\][/tex]

Next, compute [tex]\((-3)^2\)[/tex]:

[tex]\((-3)^2 = (-3) \times (-3) = 9\)[/tex]

Then, multiply by 4:

[tex]\[4 \times 9 = 36\][/tex]

So, the value of [tex]\(4p^2\)[/tex] is 36.

Step 2: Calculate [tex]\(7q^3\)[/tex]

Next, substitute [tex]\(q = -2\)[/tex] into the expression [tex]\(7q^3\)[/tex]:

[tex]\[7q^3 = 7(-2)^3\][/tex]

Next, compute [tex]\((-2)^3\)[/tex]:

[tex]\((-2)^3 = (-2) \times (-2) \times (-2) = -8\)[/tex]

Then, multiply by 7:

[tex]\[7 \times -8 = -56\][/tex]

So, the value of [tex]\(7q^3\)[/tex] is -56.

Step 3: Combine the results

Now, we simply add the two results together:

[tex]\[4p^2 + 7q^3 = 36 + (-56)\][/tex]

This simplifies to:

[tex]\[36 - 56 = -20\][/tex]

Final Answer:

So, the value of the expression [tex]\(4p^2 + 7q^3\)[/tex] when [tex]\(p = -3\)[/tex] and [tex]\(q = -2\)[/tex] is [tex]\(-20\)[/tex].
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