What is the product of 2x-1 and 2x+6? Write your answer in standard form.
Show your work.
Is the product of 2x-1 and 2x+6 equal to the product of 1x-2 and 6+2x? Explain your answer.

Answers and Step-by-step explanations:

We need to use FOIL (first, outer, inner, last) to solve this.

The first terms of each of the two expressions (2x - 1) and (2x + 6) are 2x and 2x. Multiply these together: 2x * 2x = 4x².

The outer terms are 2x and 6, respectively, and their product is 2x * 6 = 12x.

The inner terms are -1 and 2x, respectively, and their product is -1 * 2x = -2x.

The last terms are -1 and 6, respectively, and their product is -1 * 6 = -6.

Add these together:

4x² + 12x + (-2x) + (-6) = 4x² + 10x - 6

Let's see if this is equal to (1x - 2) * (6 + 2x) by expanding this one using FOIL as well:

The first terms are 1x and 6, respectively, and their product is 1x * 6 = 6x.

The outer terms are 1x and 2x, respectively, and their product is 1x * 2x = 2x².

The inner terms are -2 and 6, respectively, and their product is -2 * 6 = -12.

The last terms are -2 and 2x, respectively, and their product is -2 * 2x = -4x.

Add all these up:

6x + 2x² + (-12) + (-4x) = 2x² + 2x - 12

Clearly, 2x² + 2x - 12 is NOT the same as 4x² + 10x - 6, so (2x - 1)(2x + 6) is not equal to (x - 2)(6 + 2x).

Hope this helps!

4x² + 10x - 6

Not equal

Step-by-step explanation:

(2x - 1)(2x + 6)

4x² - 2x + 12x - 6

4x² + 10x - 6

(1x - 2)(6 + 2x)

6x - 12 + 2x² - 4x

2x² + 2x - 12

Not equal