Question

Find the product. (2 x+7)(3 x-1)

Short answer

The product of the two binomials \( (2x + 7)(3x - 1) \) is \(6x^2 + 19x - 7 \).

Step-by-step solution

Multiply First Terms

Multiply the first term of each parentheses, resulting in \(2x * 3x = 6x^2\).

Multiply Outer Terms

Next, multiply the outer terms together, bringing in \(2x * -1 = -2x\).

Multiply Inner Terms

Multiply the inner terms together, which gives \(7 * 3x = 21x\).

Multiply Last Terms

Finally, multiply the terms in the last position, resulting in \(7 * -1 = -7\).

Combine Like Terms

Combine the like terms you found when you carried out the multiplication. This results in the final answer of \(6x^2 - 2x + 21x - 7\). After combining -2x and 21x we get: \(6x^2 +19x - 7\).