How to simplify an expression by combining like terms and the distributive property | Khan Academy

The video begins by simplifying the expression 2 times (3x + 5), demonstrating that it literally means two (3x + 5)s. This is shown as (3x + 5) + (3x + 5), which simplifies to (2 times 3x) + (2 times 5).

The speaker confirms that this method is essentially the distributive property. Multiplying 2 by 3x gives 6x, and multiplying 2 by 5 gives 10, resulting in the simplified expression 6x + 10.

A more involved expression is introduced: 7 times (3y - 5) - 2 times (10 + 4y). The first part, 7 times (3y - 5), is simplified by distributing the 7, resulting in 21y - 35 (7 times 3y and 7 times -5).

For the second part of the complex expression, -2 times (10 + 4y), the speaker emphasizes treating it as distributing negative 2. This leads to -2 times 10, which is -20, and -2 times 4y, which is -8y.

The simplified expression now is 21y - 35 - 20 - 8y. The final step is to combine like terms: 21y minus 8y equals 13y, and -35 minus 20 equals -55. The completely simplified expression is 13y - 55.