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Use the Distributive Property to multiply the following polynomials:

[tex]\[ 3x^2(2x^4 - 15x) \][/tex]

[tex]\[ 3x^2(2x^4 - 15x) = \square \][/tex]


Sagot :

Sure, let's work through the process of using the Distributive Property to multiply the given polynomials step-by-step.

We start with the expression:

[tex]\[ 3x^2(2x^4 - 15x) \][/tex]

The Distributive Property states that [tex]\(a(b + c) = ab + ac\)[/tex]. In this case, we will distribute [tex]\(3x^2\)[/tex] to each term inside the parentheses.

1. Distribute [tex]\(3x^2\)[/tex] to [tex]\(2x^4\)[/tex]:
[tex]\[ 3x^2 \cdot 2x^4 = 3 \cdot 2 \cdot x^2 \cdot x^4 = 6x^{2+4} = 6x^6 \][/tex]

2. Distribute [tex]\(3x^2\)[/tex] to [tex]\(-15x\)[/tex]:
[tex]\[ 3x^2 \cdot (-15x) = 3 \cdot (-15) \cdot x^2 \cdot x = -45x^{2+1} = -45x^3 \][/tex]

Now, combine the results from each distribution step:
[tex]\[ 6x^6 - 45x^3 \][/tex]

So, the final simplified expression after applying the Distributive Property is:

[tex]\[ 3x^2(2x^4 - 15x) = 6x^6 - 45x^3 \][/tex]