### Video Transcript

Expand negative two π₯ times five π₯ cubed minus five π₯ squared.

To expand here, weβll need to use the distributive property. The distributive property tells us that if weβre multiplying π times π plus π, it will be equal to multiplying π times π and then adding that to π times π. Letβs see how we would use that here.

In our case, the π that weβre by multiplying by is negative two π₯. The π would be five times π₯ cubed and the π would be five times π₯ squared. To distribute our π here to multiply the π times π, weβll need to multiply negative two π₯ times five π₯ cubed. After that, we multiply the π term by the π term, which in our case would be multiplying negative two π₯ by five π₯ squared. Just to know before we do that, remember that you need to keep your signs the same. Weβre subtracting five π₯ squared from five π₯ cubed, so we wanna subtract here.

Weβve now added negative two π₯ times five π₯ squared. In our next step, we need to multiply negative two π₯ times five π₯ cubed equals negative 10π₯ to the fourth. Bring down our subtraction then multiply negative two π₯ times five π₯ squared. When we multiply those together, we get negative 10π₯ cubed. But because weβre subtracting a negative, we can write addition here and then bring down our 10π₯ cubed. We expanded the original problem using the distributive property to come to the final answer of negative 10π₯ to the fourth plus 10π₯ cubed.