Video: Expanding Algebraic Expressions Using Distributive Property

Expand βˆ’2π‘₯(5π‘₯Β³ βˆ’ 5π‘₯Β²).

02:26

Video Transcript

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

To expand here, we’ll need to use the distributive property. The distributive property tells us that if we’re multiplying π‘Ž times 𝑏 plus 𝑐, it will be equal to multiplying π‘Ž times 𝑏 and then adding that to π‘Ž times 𝑐. Let’s see how we would use that here.

In our case, the π‘Ž that we’re by multiplying by is negative two π‘₯. The 𝑏 would be five times π‘₯ cubed and the 𝑐 would be five times π‘₯ squared. To distribute our π‘Ž here to multiply the π‘Ž times 𝑏, we’ll need to multiply negative two π‘₯ times five π‘₯ cubed. After that, we multiply the π‘Ž term by the 𝑐 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. We’re subtracting five π‘₯ squared from five π‘₯ cubed, so we wanna subtract here.

We’ve 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 we’re 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.

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