Expanding the Expression (x+5)(2x^23x+3)
This article will demonstrate how to expand the expression (x+5)(2x^23x+3) using the distributive property, also known as the FOIL method.
Understanding the Distributive Property
The distributive property states that: a(b+c) = ab + ac.
We can apply this property to expand our expression. Think of (x+5) as a single term that needs to be multiplied by each term within the second set of parentheses.
StepbyStep Solution

Multiply (x+5) by 2x^2:
 x * 2x^2 = 2x^3
 5 * 2x^2 = 10x^2

Multiply (x+5) by 3x:
 x * 3x = 3x^2
 5 * 3x = 15x

Multiply (x+5) by 3:
 x * 3 = 3x
 5 * 3 = 15

Combine all the terms:
 2x^3 + 10x^2  3x^2  15x + 3x + 15

Simplify by combining like terms:
 2x^3 + 7x^2  12x + 15
Conclusion
By applying the distributive property, we have successfully expanded the expression (x+5)(2x^23x+3) into the simplified polynomial 2x^3 + 7x^2  12x + 15.