3-simplified-expression.jpeg "(5+n)3 Simplified Expression")
Simplifying (5 + n)³
The expression (5 + n)³ represents the cube of the binomial (5 + n). To simplify this expression, we need to expand it. Here's how:
Understanding the Concept
The expression (5 + n)³ means multiplying (5 + n) by itself three times:
(5 + n)³ = (5 + n) * (5 + n) * (5 + n)
Using the Distributive Property
We can simplify this expression using the distributive property:
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First, expand the first two factors: (5 + n) * (5 + n) = 5(5 + n) + n(5 + n) = 25 + 5n + 5n + n² = 25 + 10n + n²
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Now, multiply the result by (5 + n): (25 + 10n + n²) * (5 + n) = 5(25 + 10n + n²) + n(25 + 10n + n²) = 125 + 50n + 5n² + 25n + 10n² + n³ = n³ + 15n² + 75n + 125
Final Simplified Expression
Therefore, the simplified expression for (5 + n)³ is n³ + 15n² + 75n + 125.
This process demonstrates the power of the distributive property in expanding and simplifying expressions involving binomials raised to a power.