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]
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]
