Distributive Property Trivia Questions

Explanation
The given expression, 2(4 + 9x), can be simplified by distributing the 2 to both terms inside the parentheses. This results in 8 + 18x. Therefore, the correct answers are 8 + 18x and 18x + 8, as they both represent the simplified form of the given expression.

Explanation
The given expression is 7(x + -1). We can simplify this by distributing the 7 to both terms inside the parentheses. This gives us 7x + 7(-1), which simplifies to 7x - 7. Another way to write this is 7x + (-7), which can be further simplified to 7x - 7. Therefore, the correct answers are 7x - 7 and 7x + (-7).

Explanation
The given expression can be simplified by distributing the 12 to each term inside the parentheses. This results in 12 multiplied by a, 12 multiplied by b, and 12 multiplied by c. Therefore, the correct answer is 12a+12b+12c.

Explanation
The given expression is -9(21x + 3). To simplify this expression, we can distribute the -9 to both terms inside the parentheses. This gives us -189x - 27. Therefore, the correct answer is -189x - 27.

Explanation
The given expression is a simplified form of -5 multiplied by the expression (4x - 7). To simplify the expression, we distribute the -5 to both terms inside the parentheses, resulting in -20x + 35.

Explanation
The given expression involves combining like terms, which means adding or subtracting terms that have the same variable raised to the same power. In this case, we have -6k and 7k. When we combine these terms, we add the coefficients and keep the variable the same. Therefore, -6k + 7k equals 1k, which can also be written as just k. So, the correct answer is 1k or simply k.

Explanation
The given expression is -2x + 11 + 6x. To combine like terms, we add the coefficients of the x terms, which are -2x and 6x. Adding them gives us 4x. The constant terms, 11 and 0, remain the same. Therefore, the simplified expression is 4x + 11. Additionally, we can also write it as 11 + 4x.

Explanation
The given expression is -3x - 9 + 15x. To combine like terms, we add or subtract the coefficients of the variables that have the same power. In this case, we have -3x and 15x, which are like terms because they both have the variable x. Adding the coefficients, we get 12x. The constant terms -9 and +0 do not have any like terms to combine with, so they remain as they are. Therefore, the simplified expression is 12x - 9. Another valid way to write it is -9 + 12x.

Explanation
The given expression involves combining like terms. The first term is -5n and the second term is 3(6 + 7n). To combine like terms, we distribute the 3 to both terms inside the parentheses, resulting in 18 + 21n. Then, we combine -5n and 21n to get 16n. Therefore, the simplified expression is 18 + 16n, or 16n + 18.

Explanation
The given expression is 9a + 10(6a - 1). To simplify this expression, we can distribute the 10 to the terms inside the parentheses, which gives us 9a + 60a - 10. Combining like terms, we have 69a - 10 as the simplified expression. The alternative answer -10 + 69a is also correct, as the order of the terms does not affect the final value.