Which Form 8865 Equivalent 2023-2024

Sentence 1: Which expressions are equivalent to two times the quantity 4F + 2G? Mark all that apply. Sentence 2: So, the first one here is 8F plus 4G. Can I manipulate this somehow in a valid way so I get 8F plus 4G? Sentence 3: Well, the most obvious thing is to distribute the 2. So, 2 times this whole quantity is going to be 2 times 4F plus 2 times 2G, which is equal to 8F plus 4G. Sentence 4: So, this expression is indeed equivalent to that expression right over there. Sentence 5: Now let's see what they try to do to F times this thing right over here. Is that equivalent to that over there? Sentence 6: Well, it doesn't look like it's going to be. And if we distribute the 2F, we'll get 2F times 4, which is 8F, and 2F times 2G is plus 4FG, which is very different than 8F plus 4G. Sentence 7: So, this one is not an equivalent expression. Sentence 8: And here, we have 8F plus 2G. Well, 8F plus 2G is different than 8F plus 4G, and 8F plus 4G is an equivalent expression. Sentence 9: So, we can cross that out. Sentence 10: Lastly, we have 4 times 2F plus G. What happens if we factor 4 out of 8F plus 4G, which we already know is equivalent to our original expression? Sentence 11: If we try to factor out a 4 right over here, we divide 8 by 4 and get 2F, and divide 4G by 4 and get G. Sentence 12: Then, we have to multiply by 4 in order to not change the actual value of the expression. Sentence 13: So, all we do is divide by 4 and then multiply by 4, which doesn't...