Expanding the Expression (x+3)(x^22x+5)
This article will guide you through the process of expanding the expression (x+3)(x^22x+5). This is a common algebraic manipulation that involves the distributive property.
Understanding the Distributive Property
The distributive property states that for any numbers a, b, and c:
a(b+c) = ab + ac
This means that we can multiply a term by a sum of terms by multiplying the term with each individual term inside the sum.
Applying the Distributive Property
Let's apply the distributive property to our expression:

Multiply (x+3) by the first term in the second parenthesis, x²:
(x+3)(x²2x+5) = x(x²2x+5) + 3(x²2x+5)

Distribute x and 3 to each term inside the parentheses:
x(x²2x+5) + 3(x²2x+5) = x³  2x² + 5x + 3x²  6x + 15

Combine like terms:
x³  2x² + 5x + 3x²  6x + 15 = x³ + x²  x + 15
Final Result
Therefore, the expanded form of the expression (x+3)(x²2x+5) is x³ + x²  x + 15.
Key Takeaways
 Understanding the distributive property is crucial for expanding algebraic expressions.
 Remember to distribute each term outside the parentheses to each term inside the parentheses.
 Combine like terms after distribution to simplify the expression.