(4v+7v^2)+(7v+7v^2+7v^4)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (4v+7v^2)+(7v+7v^2+7v^4)

This article will guide you through the process of simplifying the algebraic expression (4v+7v^2)+(7v+7v^2+7v^4).

Understanding the Basics

• Terms: In algebra, terms are separated by addition or subtraction signs. In our expression, we have six terms: 4v, 7v^2, 7v, 7v^2, 7v^4.
• Coefficients: The number multiplied by a variable is called the coefficient. For example, in the term 4v, the coefficient is 4.
• Variables: Letters representing unknown values. In our expression, the variable is v.
• Exponents: The small number written above and to the right of a variable, indicating how many times the variable is multiplied by itself. For instance, in 7v^2, the exponent is 2, meaning v*v.

Combining Like Terms

To simplify the expression, we need to combine like terms, which are terms with the same variable raised to the same exponent.

1. Identify like terms:

   • 4v and 7v have the same variable 'v' raised to the power of 1.
   • 7v^2 and 7v^2 have the same variable 'v' raised to the power of 2.
   • 7v^4 is unique and has no like term.

2. Combine coefficients:

   • 4v + 7v = 11v
   • 7v^2 + 7v^2 = 14v^2

3. Write the simplified expression:

   • (4v + 7v^2) + (7v + 7v^2 + 7v^4) = 7v^4 + 14v^2 + 11v

Final Result

Therefore, the simplified form of the algebraic expression (4v+7v^2)+(7v+7v^2+7v^4) is 7v^4 + 14v^2 + 11v.