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!
