Multiplying Polynomials: (x^22x8)(x^2+3x5)
This article will guide you through the process of multiplying the two polynomials, (x^22x8) and (x^2+3x5). We'll break down the steps and provide a clear explanation.
Understanding the Problem
We are given two trinomials:
 (x^22x8)
 (x^2+3x5)
Our goal is to find the product of these two expressions.
The Multiplication Process
There are two common methods for multiplying polynomials:
 The Distributive Property: This method involves multiplying each term in the first polynomial by each term in the second polynomial.
 The FOIL Method: This is a shortcut for multiplying binomials, but it can be extended to multiplying trinomials.
Let's use the distributive property in this case:

Multiply the first term of the first polynomial (x^2) by each term of the second polynomial:
 x^2 * (x^2) = x^4
 x^2 * 3x = 3x^3
 x^2 * (5) = 5x^2

Multiply the second term of the first polynomial (2x) by each term of the second polynomial:
 2x * (x^2) = 2x^3
 2x * 3x = 6x^2
 2x * (5) = 10x

Multiply the third term of the first polynomial (8) by each term of the second polynomial:
 8 * (x^2) = 8x^2
 8 * 3x = 24x
 8 * (5) = 40

Combine all the terms:
 x^4 + 3x^3  5x^2 + 2x^3  6x^2 + 10x + 8x^2  24x + 40

Simplify by combining like terms:
 x^4 + 5x^3  3x^2  14x + 40
The Solution
Therefore, the product of the two polynomials (x^22x8) and (x^2+3x5) is x^4 + 5x^3  3x^2  14x + 40.