Question

Simplifying an expression: (x-4)(x+7) - (x-1)^2?

a. 5x - 29
b. x^2 + x - 29
c. x^2 + 5x - 29
d. x^2 + 3x - 30

Answer 1

The simplified expression is 5x - 29, obtained by expanding both terms in the original expression and combining like terms.

Step-by-step explanation:

To simplify the expression (x-4)(x+7) - (x-1)2, we need to expand both terms and then combine like terms. We will perform this step by step.

1. First, we'll expand (x-4)(x+7): x2 + 7x - 4x - 28, which simplifies to x2 + 3x - 28.
2. Next, we'll expand (x-1)2: x2 - 2x + 1.
3. Subtract the second expanded expression from the first: (x2 + 3x - 28) - (x2 - 2x + 1) becomes x2 + 3x - 28 - x2 + 2x - 1.
4. Combine like terms: 5x - 29.

The simplified expression is therefore 5x - 29, which corresponds to option a.