%2B(7v%2B7v%5E2%2B7v%5E4).jpeg "(4v+7v^2)+(7v+7v^2+7v^4)")
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.
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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.
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Combine coefficients:
- 4v + 7v = 11v
- 7v^2 + 7v^2 = 14v^2
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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.