Question
which line shows the correct and complete distribution for the problem below (2x+3)(3x-1)
A.) 2x•3+3x•-1
B.) 2x•3x-2x•-1-3•3x-3•-1
C.) 2x•3x+2x•-1+3•3x+3•-1
D.) 2x•3x+3•3x
A.) 2x•3+3x•-1
B.) 2x•3x-2x•-1-3•3x-3•-1
C.) 2x•3x+2x•-1+3•3x+3•-1
D.) 2x•3x+3•3x
Answers
GPT-4o mini
To find the correct distribution of the expression \((2x+3)(3x-1)\), we apply the distributive property (also known as the FOIL method for binomials), which includes multiplying each term in the first binomial by each term in the second binomial:
1. Multiply \(2x\) by \(3x\)
2. Multiply \(2x\) by \(-1\)
3. Multiply \(3\) by \(3x\)
4. Multiply \(3\) by \(-1\)
Now, let’s perform these multiplications:
1. \(2x \cdot 3x = 6x^2\)
2. \(2x \cdot -1 = -2x\)
3. \(3 \cdot 3x = 9x\)
4. \(3 \cdot -1 = -3\)
Now combine all these results:
\[
6x^2 - 2x + 9x - 3
\]
Combine the \(x\) terms:
\[
6x^2 + 7x - 3
\]
Now let's look through the answer choices to find the one that corresponds accurately to this process:
A.) \(2x \cdot 3 + 3x \cdot -1\) (This does not account for the full distribution).
B.) \(2x \cdot 3x - 2x \cdot -1 - 3 \cdot 3x - 3 \cdot -1\) (This has incorrect signs and additional terms, thus is incorrect).
C.) \(2x \cdot 3x + 2x \cdot -1 + 3 \cdot 3x + 3 \cdot -1\) (This is partially correct but should not split the first term's coefficient, it should stay as \(2x\)).
D.) \(2x \cdot 3x + 3 \cdot 3x\) (This does not represent both binomials as well).
Upon reviewing these choices, the closest accurate statement is choice **C**, despite its format. It properly lists the relevant multiplications, thereby representing the underlying process of distribution accurately.
So, the answer is **C)** (with the caveat that it could be better formatted).
1. Multiply \(2x\) by \(3x\)
2. Multiply \(2x\) by \(-1\)
3. Multiply \(3\) by \(3x\)
4. Multiply \(3\) by \(-1\)
Now, let’s perform these multiplications:
1. \(2x \cdot 3x = 6x^2\)
2. \(2x \cdot -1 = -2x\)
3. \(3 \cdot 3x = 9x\)
4. \(3 \cdot -1 = -3\)
Now combine all these results:
\[
6x^2 - 2x + 9x - 3
\]
Combine the \(x\) terms:
\[
6x^2 + 7x - 3
\]
Now let's look through the answer choices to find the one that corresponds accurately to this process:
A.) \(2x \cdot 3 + 3x \cdot -1\) (This does not account for the full distribution).
B.) \(2x \cdot 3x - 2x \cdot -1 - 3 \cdot 3x - 3 \cdot -1\) (This has incorrect signs and additional terms, thus is incorrect).
C.) \(2x \cdot 3x + 2x \cdot -1 + 3 \cdot 3x + 3 \cdot -1\) (This is partially correct but should not split the first term's coefficient, it should stay as \(2x\)).
D.) \(2x \cdot 3x + 3 \cdot 3x\) (This does not represent both binomials as well).
Upon reviewing these choices, the closest accurate statement is choice **C**, despite its format. It properly lists the relevant multiplications, thereby representing the underlying process of distribution accurately.
So, the answer is **C)** (with the caveat that it could be better formatted).