Expanding the Expression (5x+2)(x^23x+6)
This article will guide you through the process of expanding the expression (5x+2)(x^23x+6).
Understanding the Concept
The given expression is a product of two polynomials. To expand it, we need to apply the distributive property (also known as the FOIL method) which involves multiplying each term of the first polynomial by each term of the second polynomial.
Steps to Expand the Expression

Multiply the first term of the first polynomial by each term of the second polynomial:
 5x * x^2 = 5x^3
 5x * 3x = 15x^2
 5x * 6 = 30x

Multiply the second term of the first polynomial by each term of the second polynomial:
 2 * x^2 = 2x^2
 2 * 3x = 6x
 2 * 6 = 12

Combine all the resulting terms:
 5x^3  15x^2 + 30x + 2x^2  6x + 12

Simplify by combining like terms:
 5x^3  13x^2 + 24x + 12
Final Result
Therefore, the expanded form of the expression (5x+2)(x^23x+6) is 5x^3  13x^2 + 24x + 12.