2x^2 times x

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30-03-2025

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This article will guide you through simplifying the algebraic expression 2x² * x. We'll break down the process step-by-step, explaining the underlying rules of exponents and providing examples to solidify your understanding. This is a fundamental concept in algebra, essential for more advanced mathematical concepts.

Understanding Exponents

Before tackling the problem, let's refresh our understanding of exponents. An exponent (or power) tells us how many times a base number is multiplied by itself. For example:

• x² means x * x
• x³ means x * x * x
• x⁴ means x * x * x * x

The base number is the 'x' in these examples.

Simplifying 2x² * x

Now, let's tackle the expression: 2x² * x. We can break this down into two parts: the numerical coefficient (2) and the variable term (x² * x).

1. Dealing with the Coefficients:

The numerical coefficient is simply 2. There's nothing to simplify here.

2. Simplifying the Variable Terms:

This is where the rules of exponents come into play. When multiplying terms with the same base (in this case, 'x'), we add the exponents. Remember that 'x' has an implied exponent of 1 (x¹ = x). Therefore:

x² * x¹ = x⁽²⁺¹⁾ = x³

3. Combining the Results:

Putting the coefficient and the simplified variable term together, we get:

2x² * x = 2x³

Therefore, the simplified expression for 2x² * x is 2x³.

Further Examples

Let's explore a few more examples to reinforce the concept:

• 3y³ * 2y: Here, the coefficients multiply (3 * 2 = 6), and the exponents of 'y' are added (3 + 1 = 4). The simplified expression is 6y⁴.

• -5a²b * 3ab²: We multiply the coefficients (-5 * 3 = -15). For variables with the same base, we add exponents: a² * a¹ = a³ and b¹ * b² = b³. The final simplified expression becomes -15a³b³.

• (4x²) (2x): This example is the same as 4x² * 2x. We multiply the coefficients (4*2=8) and add the exponents of x (2+1=3). The simplified expression is 8x³.

Common Mistakes to Avoid

A common mistake is to multiply the exponents instead of adding them when multiplying terms with the same base. Remember, when multiplying terms with the same base, you add the exponents.

Conclusion

Simplifying algebraic expressions like 2x² * x is a fundamental skill in algebra. By understanding the rules of exponents and practicing with various examples, you'll master this essential concept and be well-prepared for more advanced mathematical problems. Remember the key: add the exponents when multiplying terms with the same base. The simplified form of 2x² * x is 2x³.