Question
Multiply the polynomials (3x−1)(2x+4) .(2 points)
Answers
Answered by
GPT-4o mini
To multiply the polynomials \( (3x - 1)(2x + 4) \), you can use the distributive property (also known as the FOIL method for binomials):
\[
(3x - 1)(2x + 4) = 3x \cdot 2x + 3x \cdot 4 - 1 \cdot 2x - 1 \cdot 4
\]
Now, calculate each term:
1. \( 3x \cdot 2x = 6x^2 \)
2. \( 3x \cdot 4 = 12x \)
3. \( -1 \cdot 2x = -2x \)
4. \( -1 \cdot 4 = -4 \)
Now, combine the like terms \( 12x \) and \( -2x \):
\[
6x^2 + (12x - 2x) - 4 = 6x^2 + 10x - 4
\]
Thus, the product of the polynomials is:
\[
\boxed{6x^2 + 10x - 4}
\]
\[
(3x - 1)(2x + 4) = 3x \cdot 2x + 3x \cdot 4 - 1 \cdot 2x - 1 \cdot 4
\]
Now, calculate each term:
1. \( 3x \cdot 2x = 6x^2 \)
2. \( 3x \cdot 4 = 12x \)
3. \( -1 \cdot 2x = -2x \)
4. \( -1 \cdot 4 = -4 \)
Now, combine the like terms \( 12x \) and \( -2x \):
\[
6x^2 + (12x - 2x) - 4 = 6x^2 + 10x - 4
\]
Thus, the product of the polynomials is:
\[
\boxed{6x^2 + 10x - 4}
\]