Asked by Miea
According to the Distributive Property, which is a way to rewrite the algebraic expression (3x−1)(x−4) ?
3x2+6x+4
3x(x)+3x(−4)+−1(x)+−1(−4)
3x2−5x+4
3x(−1)+3x(3x)+x(−4)+x(x)
3x2+6x+4
3x(x)+3x(−4)+−1(x)+−1(−4)
3x2−5x+4
3x(−1)+3x(3x)+x(−4)+x(x)
Answers
Answered by
GPT-4o mini
To apply the Distributive Property to the expression \((3x−1)(x−4)\), we need to distribute each term in the first parenthesis with every term in the second parenthesis.
Let's break it down step by step:
1. Distribute \(3x\) to both \(x\) and \(-4\):
\[
3x \cdot x + 3x \cdot (-4) = 3x^2 - 12x
\]
2. Distribute \(-1\) to both \(x\) and \(-4\):
\[
-1 \cdot x + (-1) \cdot (-4) = -x + 4
\]
Now combine all the terms together:
\[
3x^2 - 12x - x + 4
\]
Combine the like terms (-12x and -x):
\[
3x^2 - 13x + 4
\]
Thus, the expression can be rewritten in a simplified form. However, none of your provided options accurately represent the result of the multiplication of the expression.
The correct final answer is:
\[
3x^2 - 13x + 4
\]
If we were to compare with the provided options, the closest term would seem to be "3x^2 - 5x + 4," but keep in mind that this expression is incorrect based on the accurate application of the distributive property.
Let's break it down step by step:
1. Distribute \(3x\) to both \(x\) and \(-4\):
\[
3x \cdot x + 3x \cdot (-4) = 3x^2 - 12x
\]
2. Distribute \(-1\) to both \(x\) and \(-4\):
\[
-1 \cdot x + (-1) \cdot (-4) = -x + 4
\]
Now combine all the terms together:
\[
3x^2 - 12x - x + 4
\]
Combine the like terms (-12x and -x):
\[
3x^2 - 13x + 4
\]
Thus, the expression can be rewritten in a simplified form. However, none of your provided options accurately represent the result of the multiplication of the expression.
The correct final answer is:
\[
3x^2 - 13x + 4
\]
If we were to compare with the provided options, the closest term would seem to be "3x^2 - 5x + 4," but keep in mind that this expression is incorrect based on the accurate application of the distributive property.