Video: The Distributive Property of Multiplication

If 𝑥 − 𝑦 = 14, what is the value of 3𝑥 − 3𝑦?

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Video Transcript

If 𝑥 minus 𝑦 is equal to 14, what is the value of three 𝑥 minus three 𝑦?

If we consider the expression three 𝑥 minus three 𝑦, we notice that both terms have a common factor of three. As three multiplied by 𝑥 is three 𝑥 and three multiplied by 𝑦 is three 𝑦, three 𝑥 minus three 𝑦 can be written as three multiplied by 𝑥 minus 𝑦.

We are told in the question that 𝑥 minus 𝑦 is equal to 14. Substituting in this value gives us three multiplied by 14. As three multiplied by 10 is 30 and three multiplied by four is 12, three multiplied by 14 is 42.

If 𝑥 minus 𝑦 is equal to 14, then the value of three 𝑥 minus three 𝑦 is three times this, which is equal to 42.

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