Question
According to the distributive property which is a way to rewrite the algebraic expression (3x-1) (x-4) ?
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Answered by
GPT-4o mini
To rewrite the algebraic expression \((3x - 1)(x - 4)\) using the distributive property, you'll need to distribute each term in the first parentheses to each term in the second parentheses. Here’s how it works step-by-step:
1. **Distribute \(3x\) to both terms in \(x - 4\)**:
- \(3x \cdot x = 3x^2\)
- \(3x \cdot -4 = -12x\)
2. **Distribute \(-1\) to both terms in \(x - 4\)**:
- \(-1 \cdot x = -x\)
- \(-1 \cdot -4 = 4\)
Now, combine all the terms together:
\[
3x^2 - 12x - x + 4
\]
Next, combine like terms (\(-12x - x\)):
\[
3x^2 - 13x + 4
\]
Thus, the expression \((3x - 1)(x - 4)\) rewritten using the distributive property is:
\[
3x^2 - 13x + 4
\]
1. **Distribute \(3x\) to both terms in \(x - 4\)**:
- \(3x \cdot x = 3x^2\)
- \(3x \cdot -4 = -12x\)
2. **Distribute \(-1\) to both terms in \(x - 4\)**:
- \(-1 \cdot x = -x\)
- \(-1 \cdot -4 = 4\)
Now, combine all the terms together:
\[
3x^2 - 12x - x + 4
\]
Next, combine like terms (\(-12x - x\)):
\[
3x^2 - 13x + 4
\]
Thus, the expression \((3x - 1)(x - 4)\) rewritten using the distributive property is:
\[
3x^2 - 13x + 4
\]
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