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Multiply: [tex]5x^3\left(2x^4 - x^3 + 3\right)[/tex]

A. [tex]7x^7 - 5x^6 + 45x^3[/tex]
B. [tex]10x^7 - x^3 + 3[/tex]
C. [tex]10x^7 - 5x^6 + 15x^3[/tex]
D. [tex]10x^{12} - 5x^9 + 15x^3[/tex]

Answer :

Sure! Let's multiply the given expression step-by-step:

We need to multiply the expression:
[tex]\[ 5x^3 \left(2x^4 - x^3 + 3\right) \][/tex]

Here’s how we can do this:

1. Distribute [tex]\( 5x^3 \)[/tex] to each term inside the parenthesis.

Step-by-step multiplication:

- First, multiply [tex]\( 5x^3 \)[/tex] by [tex]\( 2x^4 \)[/tex]:
[tex]\[ 5x^3 \cdot 2x^4 = 10x^{3+4} = 10x^7 \][/tex]

- Next, multiply [tex]\( 5x^3 \)[/tex] by [tex]\( -x^3 \)[/tex]:
[tex]\[ 5x^3 \cdot -x^3 = -5x^{3+3} = -5x^6 \][/tex]

- Finally, multiply [tex]\( 5x^3 \)[/tex] by [tex]\( 3 \)[/tex]:
[tex]\[ 5x^3 \cdot 3 = 15x^3 \][/tex]

2. Combine all the results:
[tex]\[ 10x^7 - 5x^6 + 15x^3 \][/tex]

So, the product of the expression [tex]\( 5x^3 \left(2x^4 - x^3 + 3\right) \)[/tex] is:
[tex]\[ 10x^7 - 5x^6 + 15x^3 \][/tex]

Therefore, the correct answer is:
[tex]\[ 10x^7 - 5x^6 + 15x^3 \][/tex]

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