Question

multiply.
(a) (x - 3)(x - 2)
(b) (x + 5)(x - 8)

Explanation:

Step1: Apply FOIL method to \((x - 3)(x - 2)\)

\((x-3)(x - 2)=x\times x+x\times(- 2)+(-3)\times x+(-3)\times(-2)\)

Step2: Simplify the terms

\(x\times x+x\times(- 2)+(-3)\times x+(-3)\times(-2)=x^{2}-2x-3x + 6\)

Step3: Combine like - terms

\(x^{2}-2x-3x + 6=x^{2}-(2x + 3x)+6=x^{2}-5x + 6\)

Step4: Apply FOIL method to \((x + 5)(x - 8)\)

\((x + 5)(x - 8)=x\times x+x\times(-8)+5\times x+5\times(-8)\)

Step5: Simplify the terms

\(x\times x+x\times(-8)+5\times x+5\times(-8)=x^{2}-8x+5x-40\)

Step6: Combine like - terms

\(x^{2}-8x+5x-40=x^{2}-(8x - 5x)-40=x^{2}-3x-40\)

Answer:

\((x - 3)(x - 2)=x^{2}-5x + 6\); \((x + 5)(x - 8)=x^{2}-3x-40\)