(x+1)(x+3) Distributive Property

Jasonbradley

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Jun 16, 2024

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Using the Distributive Property to Expand (x+1)(x+3)

The distributive property is a fundamental concept in algebra that allows us to expand expressions involving multiplication. It states that multiplying a sum by a number is the same as multiplying each term in the sum by that number. In simpler terms:

a(b + c) = ab + ac

We can use this property to expand the expression (x+1)(x+3).

Steps to Expand (x+1)(x+3)

1. Treat (x+1) as a single term. We can rewrite the expression as: (x+1)(x+3) = (x+1) * (x+3)

2. Apply the distributive property. We multiply each term in the first set of parentheses by each term in the second set of parentheses.

   (x+1) * (x+3) = x * (x+3) + 1 * (x+3)

3. Simplify each multiplication.

   x * (x+3) + 1 * (x+3) = x^2 + 3x + x + 3

4. Combine like terms.

   x^2 + 3x + x + 3 = x^2 + 4x + 3

Therefore, the expanded form of (x+1)(x+3) is x^2 + 4x + 3.

Visualizing the Distributive Property

It can be helpful to visualize the distributive property using a diagram. Imagine a rectangle with length (x+1) and width (x+3).

[Image of a rectangle with length (x+1) and width (x+3) divided into four smaller rectangles]

The area of the rectangle is the product of its length and width: (x+1)(x+3). We can find the area of the whole rectangle by adding the areas of the four smaller rectangles:

• x * x = x^2
• x * 3 = 3x
• 1 * x = x
• 1 * 3 = 3

Adding these areas gives us x^2 + 3x + x + 3, which is the same result we obtained using the distributive property.

Conclusion

The distributive property is a powerful tool for simplifying and expanding algebraic expressions. By understanding and applying this property, we can efficiently manipulate expressions and solve equations in a variety of contexts.