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Video: Expanding Algebraic Expressions Using Distributive Property

Kathryn Kingham

Expand −2𝑥(5𝑥³ − 5𝑥²).

02:27

Video Transcript

Expand negative two 𝑥 times five 𝑥 cubed minus five 𝑥 squared.

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

In our case, the 𝑎 that we’re by multiplying by is negative two 𝑥. The 𝑏 would be five times 𝑥 cubed and the 𝑐 would be five times 𝑥 squared. To distribute our 𝑎 here to multiply the 𝑎 times 𝑏, we’ll need to multiply negative two 𝑥 times five 𝑥 cubed. After that, we multiply the 𝑎 term by the 𝑐 term, which in our case would be multiplying negative two 𝑥 by five 𝑥 squared. Just to know before we do that, remember that you need to keep your signs the same. We’re subtracting five 𝑥 squared from five 𝑥 cubed, so we wanna subtract here.

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