what is the product of x(x + 1)? 2x + x x2 + 2x 2x2 + x x2 + x

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31-03-2025

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The expression x(x + 1) represents a simple algebraic multiplication. To find the product, we need to distribute the 'x' across the terms inside the parentheses. This process, often called the distributive property or the distributive law of multiplication over addition, is a fundamental concept in algebra. Let's break it down step-by-step to determine the correct answer from the options provided: 2x + x, x² + 2x, 2x² + x, and x² + x.

Understanding the Distributive Property

The distributive property states that for any numbers a, b, and c: a(b + c) = ab + ac. In our case, a = x, b = x, and c = 1. Applying the distributive property to x(x + 1), we get:

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

Simplifying the Expression

Now, let's simplify each term:

• x * x = x² (This is because multiplying a variable by itself results in its square.)
• x * 1 = x (Multiplying any number by 1 results in the original number.)

Therefore, the simplified expression becomes:

x² + x

Comparing to the Options

Comparing our simplified expression, x² + x, to the options provided, we find that the correct answer is x² + x.

Conclusion: The Product of x(x+1)

The product of x(x + 1) is x² + x. Remember the distributive property is key to solving similar algebraic expressions. Understanding this fundamental property will help you solve more complex problems in algebra and beyond.