Question

perform the indicated operation.
$(x - 3)(x - 5) - (x + 1)(x - 4)$

explain your strategy.

Explanation:

Step1: Expand \((x - 3)(x - 5)\)

Using the FOIL method: \((x - 3)(x - 5)=x^2-5x-3x + 15=x^2-8x + 15\)

Step2: Expand \((x + 1)(x - 4)\)

Using the FOIL method: \((x + 1)(x - 4)=x^2-4x+x - 4=x^2-3x - 4\)

Step3: Subtract the two expanded expressions

\((x^2-8x + 15)-(x^2-3x - 4)=x^2-8x + 15 - x^2+3x + 4\)

Step4: Combine like terms

\(x^2 - x^2-8x+3x + 15 + 4=-5x + 19\)

Answer:

\(-5x + 19\)