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Answer :
To solve the problem and rewrite the expression without parentheses, we can distribute [tex]\(-5x^4\)[/tex] to each term inside the parentheses.
Here's a step-by-step guide:
1. Original expression:
[tex]\(-5x^4(7x^3 - 2x - 3)\)[/tex]
2. Distribute [tex]\(-5x^4\)[/tex] to each term inside the parentheses:
- Multiply [tex]\(-5x^4\)[/tex] by [tex]\(7x^3\)[/tex]:
[tex]\(-5x^4 \cdot 7x^3 = -35x^{4+3} = -35x^7\)[/tex]
- Multiply [tex]\(-5x^4\)[/tex] by [tex]\(-2x\)[/tex]:
[tex]\(-5x^4 \cdot (-2x) = 10x^{4+1} = 10x^5\)[/tex]
- Multiply [tex]\(-5x^4\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\(-5x^4 \cdot (-3) = 15x^4\)[/tex]
3. Combine the results:
Combine all the terms obtained from distributing:
[tex]\(-35x^7 + 10x^5 + 15x^4\)[/tex]
Therefore, the expression simplifies to:
[tex]\[-35x^7 + 10x^5 + 15x^4\][/tex]
This is the final simplified expression.
Here's a step-by-step guide:
1. Original expression:
[tex]\(-5x^4(7x^3 - 2x - 3)\)[/tex]
2. Distribute [tex]\(-5x^4\)[/tex] to each term inside the parentheses:
- Multiply [tex]\(-5x^4\)[/tex] by [tex]\(7x^3\)[/tex]:
[tex]\(-5x^4 \cdot 7x^3 = -35x^{4+3} = -35x^7\)[/tex]
- Multiply [tex]\(-5x^4\)[/tex] by [tex]\(-2x\)[/tex]:
[tex]\(-5x^4 \cdot (-2x) = 10x^{4+1} = 10x^5\)[/tex]
- Multiply [tex]\(-5x^4\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\(-5x^4 \cdot (-3) = 15x^4\)[/tex]
3. Combine the results:
Combine all the terms obtained from distributing:
[tex]\(-35x^7 + 10x^5 + 15x^4\)[/tex]
Therefore, the expression simplifies to:
[tex]\[-35x^7 + 10x^5 + 15x^4\][/tex]
This is the final simplified expression.
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