(3x^2y^4)(4xy^2)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (3x²y⁴)(4xy²)

This article will guide you through simplifying the expression (3x²y⁴)(4xy²).

Understanding the Basics

Before we begin, let's review some key concepts:

• Coefficients: Numbers that multiply variables. In our expression, the coefficients are 3 and 4.
• Variables: Letters representing unknown values. Here, the variables are x and y.
• Exponents: Small numbers written above and to the right of variables indicating how many times the variable is multiplied by itself. For example, x² means x multiplied by itself (x * x).

Simplifying the Expression

1. Multiply the coefficients: 3 * 4 = 12

2. Multiply the x terms: x² * x = x³ (Remember, when multiplying exponents with the same base, you add the powers).

3. Multiply the y terms: y⁴ * y² = y⁶ (Again, add the powers).

The Result

By combining the results from steps 1, 2, and 3, we get the simplified expression: 12x³y⁶.

Conclusion

Therefore, the simplified form of (3x²y⁴)(4xy²) is 12x³y⁶. This process illustrates how to combine coefficients, variables, and exponents when multiplying expressions with multiple terms.