Final answer:
The true options from the provided binomial properties are A (simple arithmetic), C (tautology), E (tautology), and F (tautology), where terms are correctly added or shown to be equal to themselves. Options B and D do not correctly apply algebraic properties.
Step-by-step explanation:
The question seems to be about identifying which of the provided equations show correct usage of binomial properties or are examples of correct addition or multiplication of terms in algebra. To check which option is true, we evaluate each option:
- A) 12 + 20 = 32: This is a simple arithmetic addition and is correct.
- B) 22w + 55 = 77w: This would only be correct if 22w and 55w were terms that could be combined, but since 55 is not attached to the variable w, this statement is incorrect.
- C) 15g - 21 = 15g - 21: This is an equation stating a term is equal to itself, which is tautologically true.
- D) 8n + 14 = 22n: This would only be correct if the terms on both sides could be combined into 22n, which they cannot since 14 is not a multiple of n.
- E) 9w - 12 = 9w - 12: This is another equation stating a term is equal to itself, which is always true.
- F) 2k + 6 = 2k + 6: Similarly, this states a term is equal to itself and is true.
Options A, C, E, and F are true statements. Options B and D are not correct applications of algebraic principles for adding or combining like terms.