Multiplying Polynomials: (−p2+4p−3)(p2+2)
This article will guide you through the process of multiplying the polynomials (−p2+4p−3)(p2+2). We will use the distributive property and some helpful tips to simplify the expression.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. In other words, for any numbers a, b, and c:
a(b + c) = ab + ac
Applying the Distributive Property to Polynomial Multiplication
We can use the distributive property to multiply polynomials. We will treat each term of one polynomial as if it were a separate number and distribute it across the other polynomial.
Let's break down the multiplication:

Distribute (p^2) across (p^2 + 2):
(p^2)(p^2 + 2) = p^4  2p^2

Distribute (4p) across (p^2 + 2):
(4p)(p^2 + 2) = 4p^3 + 8p

Distribute (3) across (p^2 + 2):
(3)(p^2 + 2) = 3p^2  6
Combining the Terms
Now, we have three separate expressions. Let's combine them by adding their corresponding terms:
(p^4  2p^2) + (4p^3 + 8p) + (3p^2  6)
Simplifying the expression, we get:
p^4 + 4p^3  5p^2 + 8p  6
Therefore, the product of (−p2+4p−3)(p2+2) is p^4 + 4p^3  5p^2 + 8p  6.
Key Points to Remember:
 Distributive property is your best friend: Always remember to distribute each term of one polynomial across all the terms of the other.
 Combine like terms: After distributing, simplify the expression by combining terms with the same variable and exponent.
By following these steps, you can confidently multiply any pair of polynomials.