(p2%2B2).jpeg "(−p2+4p−3)(p2+2)")
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:
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Distribute (-p^2) across (p^2 + 2):
(-p^2)(p^2 + 2) = -p^4 - 2p^2
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Distribute (4p) across (p^2 + 2):
(4p)(p^2 + 2) = 4p^3 + 8p
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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.