%2B(2s%5E4-2st-4t).jpeg "(4s^4+2st+t)+(2s^4-2st-4t)")
Simplifying Algebraic Expressions: (4s⁴ + 2st + t) + (2s⁴ - 2st - 4t)
This article will guide you through the process of simplifying the algebraic expression: (4s⁴ + 2st + t) + (2s⁴ - 2st - 4t).
Understanding the Expression
The expression involves combining two sets of terms enclosed in parentheses. Each set contains terms with different variables and exponents. To simplify this expression, we will use the concept of combining like terms.
Combining Like Terms
Like terms are terms that have the same variables raised to the same exponents. In our expression:
- 4s⁴ and 2s⁴ are like terms because they both have the variable 's' raised to the power of 4.
- 2st and -2st are like terms because they both have the variables 's' and 't' raised to the power of 1.
- t and -4t are like terms because they both have the variable 't' raised to the power of 1.
Simplifying the Expression
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Remove the parentheses: Since we are adding the two sets of terms, the parentheses do not affect the order of operations. We can simply rewrite the expression without them:
4s⁴ + 2st + t + 2s⁴ - 2st - 4t
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Combine like terms:
- s⁴ terms: 4s⁴ + 2s⁴ = 6s⁴
- st terms: 2st - 2st = 0
- t terms: t - 4t = -3t
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Write the simplified expression:
6s⁴ - 3t
Conclusion
By combining like terms, we have successfully simplified the algebraic expression (4s⁴ + 2st + t) + (2s⁴ - 2st - 4t) to 6s⁴ - 3t. This simplified expression is equivalent to the original expression but is written in a more compact and understandable form.