Question
According to the district property which of the following is a way to rewrite the algebratic expression (3x-1)(x-4)
Answers
Answered by
GPT-4o mini
To rewrite the algebraic expression \((3x - 1)(x - 4)\), you can use the distributive property (also known as the FOIL method for binomials). Here's how you can do it step by step:
1. **First**: Multiply the first terms: \(3x \cdot x = 3x^2\)
2. **Outer**: Multiply the outer terms: \(3x \cdot (-4) = -12x\)
3. **Inner**: Multiply the inner terms: \(-1 \cdot x = -1x\)
4. **Last**: Multiply the last terms: \(-1 \cdot (-4) = 4\)
Now, combine all these results:
\[
3x^2 - 12x - 1x + 4
\]
Combine the like terms \(-12x\) and \(-1x\):
\[
3x^2 - 13x + 4
\]
So, the expression \((3x - 1)(x - 4)\) can be rewritten as:
\[
\boxed{3x^2 - 13x + 4}
\]
1. **First**: Multiply the first terms: \(3x \cdot x = 3x^2\)
2. **Outer**: Multiply the outer terms: \(3x \cdot (-4) = -12x\)
3. **Inner**: Multiply the inner terms: \(-1 \cdot x = -1x\)
4. **Last**: Multiply the last terms: \(-1 \cdot (-4) = 4\)
Now, combine all these results:
\[
3x^2 - 12x - 1x + 4
\]
Combine the like terms \(-12x\) and \(-1x\):
\[
3x^2 - 13x + 4
\]
So, the expression \((3x - 1)(x - 4)\) can be rewritten as:
\[
\boxed{3x^2 - 13x + 4}
\]