Question

Karen simplified the expression below:

(x + 4)(4x - 1) + 5(x - 3)(x + 2)(x - 3)

A. What was her error? (fully describe)
B. What is the correct resulting expression?

Answer 1

The error in Karen's simplification is that she did not fully distribute the terms in the expression. The correct resulting expression is obtained by combining like terms and simplifying further if possible.

Step-by-step explanation:

The error in Karen's simplification is that she did not fully distribute the terms in the expression. To simplify the expression correctly, we need to use the distributive property to multiply each term in the first set of parentheses, (x + 4), by each term in the second set of parentheses, (4x - 1). Similarly, we need to multiply each term in (x - 3) by each term in (x + 2)(x - 3). Here are the steps to simplify the expression correctly:

1. Distribute the terms in the first set of parentheses: (x + 4)(4x - 1) = x(4x - 1) + 4(4x - 1)
2. Distribute the terms in the second set of parentheses: 5(x - 3)(x + 2)(x - 3) = 5(x - 3)(x + 2)x - 5(x - 3)(x + 2)3
3. Simplify each term: x(4x - 1) + 4(4x - 1) + 5(x - 3)(x + 2)x - 5(x - 3)(x + 2)3

The correct resulting expression is obtained by combining like terms and simplifying further if possible.