3 min read Jun 17, 2024

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:

  1. Distribute (-p^2) across (p^2 + 2):

    (-p^2)(p^2 + 2) = -p^4 - 2p^2

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

    (4p)(p^2 + 2) = 4p^3 + 8p

  3. 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.

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