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Multiplying Polynomials

Instructions: Simplify the polynomial expression.

[tex]5x^3(8x^2 - 6x - 7)[/tex]

Answer: [tex]40x^5 - 30x^4 - 35x^3[/tex]

Answer :

To simplify the polynomial expression [tex]\(5x^3(8x^2 - 6x - 7)\)[/tex], we need to distribute [tex]\(5x^3\)[/tex] to each term inside the parentheses. Let's go through the steps:

1. Multiply [tex]\(5x^3\)[/tex] with [tex]\(8x^2\)[/tex]:

[tex]\[
5x^3 \cdot 8x^2 = 40x^{3+2} = 40x^5
\][/tex]

2. Multiply [tex]\(5x^3\)[/tex] with [tex]\(-6x\)[/tex]:

[tex]\[
5x^3 \cdot (-6x) = -30x^{3+1} = -30x^4
\][/tex]

3. Multiply [tex]\(5x^3\)[/tex] with [tex]\(-7\)[/tex]:

[tex]\[
5x^3 \cdot (-7) = -35x^3
\][/tex]

Now, let's write down the simplified polynomial by adding these terms together:

[tex]\[
40x^5 - 30x^4 - 35x^3
\][/tex]

So, the simplified expression is:

Answer: [tex]\(40x^5 - 30x^4 - 35x^3\)[/tex]

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