Asked by T-Swizzle
Show the correct and complete distribution for the problem: (2x + 3) (3x - 1) Make it the longest
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Answered by
GPT-4o mini
To find the complete distribution of the expression \((2x + 3)(3x - 1)\), we will apply the distributive property, also known as the FOIL method (First, Outer, Inner, Last).
1. **First**: Multiply the first terms in each binomial:
\[
2x \cdot 3x = 6x^2
\]
2. **Outer**: Multiply the outer terms:
\[
2x \cdot (-1) = -2x
\]
3. **Inner**: Multiply the inner terms:
\[
3 \cdot 3x = 9x
\]
4. **Last**: Multiply the last terms:
\[
3 \cdot (-1) = -3
\]
Now, we combine all the results from the above steps:
\[
6x^2 - 2x + 9x - 3
\]
Next, we can combine like terms (the linear terms \(-2x\) and \(9x\)):
\[
6x^2 + 7x - 3
\]
Thus, the complete distribution of \((2x + 3)(3x - 1)\) is:
\[
\boxed{6x^2 + 7x - 3}
\]
1. **First**: Multiply the first terms in each binomial:
\[
2x \cdot 3x = 6x^2
\]
2. **Outer**: Multiply the outer terms:
\[
2x \cdot (-1) = -2x
\]
3. **Inner**: Multiply the inner terms:
\[
3 \cdot 3x = 9x
\]
4. **Last**: Multiply the last terms:
\[
3 \cdot (-1) = -3
\]
Now, we combine all the results from the above steps:
\[
6x^2 - 2x + 9x - 3
\]
Next, we can combine like terms (the linear terms \(-2x\) and \(9x\)):
\[
6x^2 + 7x - 3
\]
Thus, the complete distribution of \((2x + 3)(3x - 1)\) is:
\[
\boxed{6x^2 + 7x - 3}
\]
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