Question

Simplify the expression: (x + 2)³

Options:
Option 1: x³ + 6x² + 12x + 8
Option 2: x³ + 8x² + 16x + 8
Option 3: x³ + 3x² + 6x + 2
Option 4: x³ + 4x² + 8x + 8

Answer 1

To simplify the expression (x + 2)³, use the formula for expanding a binomial raised to a power and distribute.

Step-by-step explanation:

To simplify the expression (x + 2)³, we can use the formula for expanding a binomial raised to a power. In this case, we have (x + 2)³ = (x + 2)(x + 2)(x + 2).

Expanding this using the distributive property, we get x(x + 2)(x + 2) + 2(x + 2)(x + 2) = x³ + 2x² + 2x² + 4x + 2x + 4 + 8 = x³ + 4x² + 8x + 8.

Therefore, the correct option is Option 4: x³ + 4x² + 8x + 8.

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