Video: Determining the Number of Terms and Factors an Algebraic Expression Consists Of

What does the expression 2𝑎𝑏 + 3𝑐𝑑 consist of? [A] 2 terms of 1 factor [B] 2 terms of 2 factors [C] 2 terms of 3 factors [D] 3 terms of 1 factor [E] 3 terms of 2 factors

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Video Transcript

What does the expression two 𝑎𝑏 plus three 𝑐𝑑 consist of? a) Two terms of one factor. b) Two terms of two factors. c) Two terms of three factors. d) Three terms of one factor. Or e) Three terms of two factors.

Before you move on, it seems like it would be helpful to define the words term and factor. A term is a single number or variable or numbers and variables multiplied together. And a factor are what we multiply together to get another value.

Two 𝑎𝑏 are numbers and variables being multiplied together. That’s a term. Three 𝑐𝑑 are numbers and variables multiplied together, which is another term.

We’ll eliminate the two answer choices that say three terms. And what’s happening within these terms. Another way we could say this is what is being multiplied together to get two 𝑎𝑏, two times 𝑎 times 𝑏. And that means two 𝑎𝑏 is made up of three factors. Three 𝑐𝑑 is made up of three times 𝑐 times 𝑑, which is again three factors, two terms of three factors each.

For us, that’s answer choice c, two terms of three factors.