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

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (-p^2+4p-3)(p^2+2)

This article will walk through the steps of expanding the given expression: (-p^2+4p-3)(p^2+2)

Expanding using the distributive property

We can expand this expression by using the distributive property (sometimes called FOIL for First, Outer, Inner, Last). This means multiplying each term in the first set of parentheses by each term in the second set of parentheses.

Let's break it down step-by-step:

1. Multiply -p^2 by each term in the second set of parentheses:

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

2. Multiply 4p by each term in the second set of parentheses:

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

3. Multiply -3 by each term in the second set of parentheses:

   • (-3)(p^2) = -3p^2
   • (-3)(2) = -6

4. Combine all the terms: -p^4 - 2p^2 + 4p^3 + 8p - 3p^2 - 6

5. Rearrange the terms in descending order of their exponents:

   • -p^4 + 4p^3 - 5p^2 + 8p - 6

Simplified Expression

Therefore, the expanded form of (-p^2+4p-3)(p^2+2) is -p^4 + 4p^3 - 5p^2 + 8p - 6.