# Video: Recognizing Equivalent Expressions

Which of the following expressions is equivalent to −11(3 + 12𝑥)? [A] −33 − 132𝑥 [B] 33 + 132𝑥 [C] −33 + 132𝑥 [D] −33 + 11𝑥 [E] −33 − 11𝑥

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### Video Transcript

Which of the following expressions is equivalent to negative 11 multiplied by three plus 12𝑥? Is it A) negative 33 minus 132𝑥, B) 33 plus 132𝑥, C) negative 33 plus 132𝑥, D) negative 33 plus 11𝑥, or E) negative 33 minus 11𝑥?

In order to answer this question, we need to distribute the parenthesis, otherwise known as expanding the bracket. This means that we need to multiply the term outside by each of the terms inside the bracket. Firstly, we need to multiply negative 11 by three. Multiplying a negative number by a positive number gives us a negative answer. And 11 multiplied by three is equal to 33. Therefore, negative 11 multiplied by three is equal to negative 33.

We also need to multiply negative 11 by 12𝑥. Once again, we have a negative and a positive term. This means that our answer will be negative. 11 multiplied by 12 is 132. This means that negative 11 multiplied by 12𝑥 is equal to negative 132𝑥. The expression that is equivalent to negative 11 multiplied by three plus 12𝑥 is negative 33 minus 132𝑥. This was option A out of our five options.

An alternative method would have been to have factorized each of the five options and see which one gives us an answer of negative 11 multiplied by three plus 12𝑥. The two terms negative 33 and negative 132𝑥 have a highest common factor of negative 11. Therefore, we can take this outside of the parentheses. Negative 11 multiplied by three is equal to negative 33. Therefore, the first term inside the parentheses is three. Negative 11 multiplied by 12𝑥 is equal to negative 132𝑥. Therefore, the second term in the parentheses is 12𝑥. This proves that option A was the correct answer.