Question Video: Simplifying Algebraic Expressions Mathematics

Simplify the expression 6 ⋅ (𝑥 ⋅ 8).

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Video Transcript

Remember this dot is used interchangeably with the multiplication symbol. And so, to simplify the expression given, we’re going to recall some of the properties of multiplication. Firstly, the associative property of multiplication. This says that when three or more numbers are multiplied, the product is the same, no matter how those numbers are grouped. And so, we don’t really need the parentheses here. It will be the same as just doing six times 𝑥 times eight. Then, the commutative property says that the product will be the same even if we switch the numbers around. For instance, three times four is the same as four times three. And so, we’re going to switch the 𝑥 and the eight around and rewrite our problem as six times eight times 𝑥. And then, of course, since the grouping doesn’t really matter, we can evaluate six times eight. Six times eight is 48, so this becomes 48 times 𝑥. And of course, we know that we can simply write that as 48𝑥. So, when we simplify the expression six times eight times 𝑥, we get 48𝑥.

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