(x+8)(x+8)(x+8)

Jasonbradley

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Jun 17, 2024

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Expanding (x+8)(x+8)(x+8)

This expression represents the cube of the binomial (x+8). To expand it, we can use the following methods:

1. Repeated Multiplication

We can expand the expression by multiplying it out step-by-step:

1. First, multiply the first two binomials: (x+8)(x+8) = x² + 8x + 8x + 64 = x² + 16x + 64

2. Then, multiply the result by the remaining binomial: (x² + 16x + 64)(x+8) = x³ + 16x² + 64x + 8x² + 128x + 512

3. Finally, combine like terms: x³ + 24x² + 192x + 512

2. Binomial Theorem

The Binomial Theorem provides a general formula for expanding any power of a binomial:

(a + b)ⁿ = Σ (n choose k) a^(n-k) b^k

Where:

• (n choose k) represents the binomial coefficient, calculated as n! / (k! * (n-k)!).

Applying this to our case, we have:

(x + 8)³ = (3 choose 0) x³ 8⁰ + (3 choose 1) x² 8¹ + (3 choose 2) x¹ 8² + (3 choose 3) x⁰ 8³

Simplifying this, we get:

(x + 8)³ = x³ + 24x² + 192x + 512

Summary

Both methods lead to the same result:

The expanded form of (x+8)(x+8)(x+8) is x³ + 24x² + 192x + 512.