Question Video: Using the Distributive Property of Multiplication to Expand Expressions Containing Brackets

Expand βˆ’3π‘₯(4𝑦 βˆ’ 7π‘₯).

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Video Transcript

Expand negative three π‘₯ multiplied by four 𝑦 minus seven π‘₯.

In order to expand this bracket, we need to multiply the term outside the bracket by each of the terms inside. We need to multiply negative three π‘₯ by four 𝑦 and negative three π‘₯ by negative seven π‘₯. Negative three π‘₯ multiplied by four 𝑦 is equal to negative 12π‘₯𝑦, as negative three multiplied by four is equal to negative 12. A negative number multiplied by a positive number gives a negative answer. Negative three π‘₯ multiplied by negative seven π‘₯ is equal to 21π‘₯ squared, as negative three multiplied by negative seven is equal to 21. Multiplying two negative numbers gives us a positive answer. And π‘₯ multiplied by π‘₯ is equal to π‘₯ squared. This means that the expansion of negative three π‘₯ multiplied by four 𝑦 minus seven π‘₯ is equal to negative 12π‘₯𝑦 plus 21π‘₯ squared.

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