3-write-the-simplified-expression.jpeg "(5+n)3 Write The Simplified Expression")
Simplifying the Expression (5 + n)³
In mathematics, simplifying an expression means rewriting it in a more compact and understandable form while maintaining its equivalence. Let's explore how to simplify the expression (5 + n)³.
Understanding the Concept
(5 + n)³ represents the product of (5 + n) multiplied by itself three times: (5 + n)³ = (5 + n) * (5 + n) * (5 + n)
To simplify this expression, we need to apply the distributive property and perform the necessary multiplications.
Step-by-Step Simplification
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Expand the first two factors: (5 + n) * (5 + n) = 25 + 5n + 5n + n² = 25 + 10n + n²
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Multiply the result by the remaining factor (5 + n): (25 + 10n + n²) * (5 + n) = 125 + 50n + 5n² + 25n + 10n² + n³
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Combine like terms: 125 + 50n + 5n² + 25n + 10n² + n³ = n³ + 15n² + 75n + 125
Conclusion
Therefore, the simplified expression for (5 + n)³ is n³ + 15n² + 75n + 125. Remember that this process involves applying the distributive property and combining like terms to arrive at the most concise and understandable form.