Asked by Ebaybu
An expression is shown.
(-29 - 10x^2 + 12x) + 3x(5x - 4)
Rewrite an equivalent expression with the fewest terms possible.
(-29 - 10x^2 + 12x) + 3x(5x - 4)
Rewrite an equivalent expression with the fewest terms possible.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To rewrite the expression \((-29 - 10x^2 + 12x) + 3x(5x - 4)\) with the fewest terms possible, we will first distribute the \(3x\) in the second part of the expression and then combine like terms.
1. **Distribute \(3x\) to \(5x - 4\):**
\[
3x(5x - 4) = 15x^2 - 12x
\]
2. **Substitute this back into the original expression:**
\[
(-29 - 10x^2 + 12x) + (15x^2 - 12x)
\]
3. **Combine like terms:**
- For \(x^2\) terms: \(-10x^2 + 15x^2 = 5x^2\)
- For \(x\) terms: \(12x - 12x = 0\)
- The constant term remains: \(-29\)
4. **Write the final result:**
The equivalent expression with the fewest terms possible is:
\[
5x^2 - 29
\]
1. **Distribute \(3x\) to \(5x - 4\):**
\[
3x(5x - 4) = 15x^2 - 12x
\]
2. **Substitute this back into the original expression:**
\[
(-29 - 10x^2 + 12x) + (15x^2 - 12x)
\]
3. **Combine like terms:**
- For \(x^2\) terms: \(-10x^2 + 15x^2 = 5x^2\)
- For \(x\) terms: \(12x - 12x = 0\)
- The constant term remains: \(-29\)
4. **Write the final result:**
The equivalent expression with the fewest terms possible is:
\[
5x^2 - 29
\]
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