Question
Simplify the following expression \[ -(x+5)(x+8) \]
Ask by Klein Knight. in South Africa
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \(-x^2 - 13x - 40\).
Solution
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The Deep Dive
To simplify the expression \( -(x+5)(x+8) \), we first need to expand the product within the parentheses. Using the distributive property (also known as FOIL for binomials), we calculate: \[ (x+5)(x+8) = x^2 + 8x + 5x + 40 = x^2 + 13x + 40 \] Now, we apply the negative sign from the original expression: \[ -(x^2 + 13x + 40) = -x^2 - 13x - 40 \] So the simplified expression is: \[ -x^2 - 13x - 40 \]
