Show the correct and complete distribution for the problem: (2x + 3) (3x - 1)

Answer 1

To find the distribution of the expression \((2x + 3)(3x - 1)\), we will use the distributive property (also known as the FOIL method for binomials).

1. First: Multiply the first terms of 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 of each binomial: \[ 3 \cdot (-1) = -3 \]

Now, combine all these results: \[ 6x^2 - 2x + 9x - 3 \]

Next, combine like terms: \[ 6x^2 + (9x - 2x) - 3 = 6x^2 + 7x - 3 \]

Thus, the complete distribution for \((2x + 3)(3x - 1)\) is: \[ \boxed{6x^2 + 7x - 3} \]

Answer 2

what was the first distribute process?

Answer 3

The first step in the distribution process for the expression \((2x + 3)(3x - 1)\) involves multiplying each term in the first binomial \((2x + 3)\) by each term in the second binomial \((3x - 1)\).

Here's how it breaks down step by step:

1. Multiply the first terms (2x and 3x):

   • \(2x \cdot 3x = 6x^2\)

2. Multiply the outer terms (2x and -1):

   • \(2x \cdot (-1) = -2x\)

3. Multiply the inner terms (3 and 3x):

   • \(3 \cdot 3x = 9x\)

4. Multiply the last terms (3 and -1):

   • \(3 \cdot (-1) = -3\)

So, the first distribution process involves taking each term from the first binomial and multiplying it by each term from the second binomial, as described above.

The result from these multiplications gives you: \[ 6x^2 - 2x + 9x - 3 \]

This result is then simplified by combining like terms to produce the final expression: \[ 6x^2 + 7x - 3 \]