Question
(5x-2)(4x+8)+3x^2-9x
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Answered by
GPT-4o mini
To simplify the expression \((5x-2)(4x+8)+3x^2-9x\), we'll first expand the product \((5x-2)(4x+8)\) and then combine like terms.
1. **Expand \((5x-2)(4x+8)\)**:
\[
(5x)(4x) + (5x)(8) + (-2)(4x) + (-2)(8)
\]
\[
= 20x^2 + 40x - 8x - 16
\]
\[
= 20x^2 + (40x - 8x) - 16
\]
\[
= 20x^2 + 32x - 16
\]
2. **Now, add \(3x^2 - 9x\)**:
We combine this with the expanded form:
\[
20x^2 + 32x - 16 + 3x^2 - 9x
\]
3. **Combine like terms**:
- Combine \(20x^2\) and \(3x^2\):
\[
20x^2 + 3x^2 = 23x^2
\]
- Combine \(32x\) and \(-9x\):
\[
32x - 9x = 23x
\]
So the expression becomes:
\[
23x^2 + 23x - 16
\]
Thus, the simplified expression is:
\[
\boxed{23x^2 + 23x - 16}
\]
1. **Expand \((5x-2)(4x+8)\)**:
\[
(5x)(4x) + (5x)(8) + (-2)(4x) + (-2)(8)
\]
\[
= 20x^2 + 40x - 8x - 16
\]
\[
= 20x^2 + (40x - 8x) - 16
\]
\[
= 20x^2 + 32x - 16
\]
2. **Now, add \(3x^2 - 9x\)**:
We combine this with the expanded form:
\[
20x^2 + 32x - 16 + 3x^2 - 9x
\]
3. **Combine like terms**:
- Combine \(20x^2\) and \(3x^2\):
\[
20x^2 + 3x^2 = 23x^2
\]
- Combine \(32x\) and \(-9x\):
\[
32x - 9x = 23x
\]
So the expression becomes:
\[
23x^2 + 23x - 16
\]
Thus, the simplified expression is:
\[
\boxed{23x^2 + 23x - 16}
\]
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