What you’ll learn
Multiply simple polynomials.
Key idea
Keep all six products before combining cubic, square, linear and constant powers.
Distribute both linear-factor terms across all three quadratic addends, then combine powers up to degree three.
Worked example
Enter the exact value or ordered values in the format requested below.
Expand (x²-6x-5)(x+2); enter collected polynomial of degree three.
- Multiply quadratic by x to obtain x³-6x²-5x; multiply by 2 to obtain 2x²-12x-10.
- Combine matching powers to get x³-4x²-17x-10; missing b gives square coefficient b+(2)=-4 and linear coefficient -5+2b=-17.
Answer: x³-4x²-17x-10
Quick Check
Evaluate a worked attempt at multiply simple polynomials, identify the first invalid step, and provide the correction.
Expand (x²-6x-2)(x-6): Step 1 multiplies by x to get x³-6x²-2x. Step 2 multiplies by -6 but omits -6x², yielding x³-6x²+34x+12. Locate the first invalid step and repair the cubic.