(a-5).jpeg "(2a^2+7a-10)(a-5)")
Multiplying Polynomials: (2a^2 + 7a - 10)(a - 5)
This article will guide you through the steps of multiplying the polynomials (2a^2 + 7a - 10) and (a - 5). We'll use the distributive property to expand the product and simplify the resulting expression.
1. The Distributive Property
The distributive property states that for any numbers a, b, and c: a(b + c) = ab + ac
We'll apply this property twice to multiply our polynomials.
2. Expanding the Product
First, distribute the (a - 5) term across the entire (2a^2 + 7a - 10) expression:
(2a^2 + 7a - 10)(a - 5) = a(2a^2 + 7a - 10) - 5(2a^2 + 7a - 10)
Now, distribute the a and the -5 terms individually:
- a(2a^2 + 7a - 10) = 2a^3 + 7a^2 - 10a
- -5(2a^2 + 7a - 10) = -10a^2 - 35a + 50
3. Combining Like Terms
Finally, combine the like terms from each distribution to obtain the simplified expression:
(2a^3 + 7a^2 - 10a) + (-10a^2 - 35a + 50) = 2a^3 - 3a^2 - 45a + 50
4. The Result
Therefore, the product of (2a^2 + 7a - 10) and (a - 5) is 2a^3 - 3a^2 - 45a + 50.