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

Video Transcript

Expand negative three 𝑥 multiplied by four 𝑦 minus seven 𝑥.

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 𝑥 by four 𝑦 and negative three 𝑥 by negative seven 𝑥. Negative three 𝑥 multiplied by four 𝑦 is equal to negative 12𝑥𝑦, 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 𝑥 multiplied by negative seven 𝑥 is equal to 21𝑥 squared, as negative three multiplied by negative seven is equal to 21. Multiplying two negative numbers gives us a positive answer. And 𝑥 multiplied by 𝑥 is equal to 𝑥 squared. This means that the expansion of negative three 𝑥 multiplied by four 𝑦 minus seven 𝑥 is equal to negative 12𝑥𝑦 plus 21𝑥 squared.