Question Video: Expanding Single Bracket Expressions

Expand −11(5 + 7𝑥).

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Video Transcript

Expand negative 11 multiplied by five plus seven 𝑥.

In order to expand a bracket or parentheses, we need to multiply the term outside by each of the terms inside. In this question, we need to multiply negative 11 by five and negative 11 by seven 𝑥. Multiplying a negative number by a positive number gives us a negative answer. Therefore, negative 11 multiplied by five is equal to negative 55. The first term in our expansion is negative 55.

Negative 11 multiplied by seven is equal to negative 77. Therefore, negative 11 multiplied by seven 𝑥 is negative 77𝑥. This means that the second term in the expansion is negative 77𝑥. Multiplying negative 11 by five plus seven 𝑥 gives us negative 55 minus 77𝑥.

We can check this answer by factorising our expression to see if we get the original expression. The highest common factor of negative 55 and negative 77 is negative 11. Therefore, we can take this out of the parentheses. Negative 55 divided by negative 11 is equal to five. Therefore, this is the first term inside the bracket. Negative 77 divided by negative 11 is seven. Therefore, the second term is seven 𝑥. As this is the same as our original expression, we know that the answer negative 55 minus 77𝑥 is correct.

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