Question

James is building a post for his birdhouse. To find the correct dimensions, he needs to expand this expression: (x - 4)(x - 8)(x - 2) Select the equivalent expression written in the format ax³ + bx² + cx + d. a) x³ + 6x² + 24x - 64 b) x³ - 6x² - 24x + 64 c) x³ - 14x² + 56x -64 d) x³ + 14x² - 56x + 64

Answer 1

To expand (x - 4)(x - 8)(x - 2), first multiply the first two binomials, then multiply the result with the last binomial. The expanded expression is x³ - 14x² + 56x - 64.

Step-by-step explanation:

To find out the correct dimensions for James' birdhouse post, you need to expand this expression: (x - 4)(x - 8)(x - 2). This is essentially calculating the product of three binomials. To carry out this operation, follow these steps:

1. Expand the first two binomials: (x - 4)(x - 8) to get x² - 12x + 32.
2. Next, multiply the result from step 1 with the third binomial to get your final result: (x² - 12x + 32)(x - 2).
3. This multiplies out to the equivalent expression x³ - 14x² + 56x - 64.

Therefore, the factored expression (x - 4)(x - 8)(x - 2) is equivalent to the expanded expression x³ - 14x² + 56x - 64, which matches option c) in your question.

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