Question Video: Multiplying a Monomial by a Binomial Mathematics

Video Transcript

Calculate three times 𝑥 minus 𝑥 cubed.

First, we can copy down what we’ve been given. We have the expression 𝑥 minus 𝑥 cubed and then the whole number or the monomial three. We’re trying to multiply these values together. And to do that, we should use the distributive property. It tells us that 𝑎 times 𝑏 plus 𝑐 is equal to 𝑎 times 𝑏 plus 𝑎 times 𝑐. Often when we’re working with the distributive property, we represent it with arrows. It means we need to multiply three by 𝑥. And we should be careful with our second term. It’s helpful to rewrite this subtraction as plus and negative as we need to multiply three by negative 𝑥 cubed. So we get something like this.

Now, three times 𝑥 equals three 𝑥 and three times negative 𝑥 cubed would equal negative three 𝑥 cubed. Three times 𝑥 minus 𝑥 cubed is equal to three 𝑥 minus three 𝑥 cubed. We need to be really careful here. Some people might see these two three coefficients and think that they can do some subtraction, but that is not possible. Remember, we cannot add or subtract values like this when their exponents are different. And that means three 𝑥 minus three 𝑥 cubed is in its simplest form.