What you’ll learn
Multiply binomials.
Key idea
Include both cross products and combine only like powers; first and last products alone are incomplete.
All four products contribute; include both signed cross terms and require expanded result.
Worked example
Enter the exact value or ordered values in the format requested below.
Expand (x-7)(x-5); enter collected polynomial.
- All four products are x², -5x, -7x, 35; cross terms sum to -12x.
- Collected result x²-12x+35; missing constant k obeys -7k=35 and -7+k=-12, giving k=-5.
Answer: x²-12x+35
Quick Check
Evaluate a worked attempt at multiply binomials, identify the first invalid step, and provide the correction.
Expand (x-5)(x+2): Step 1 obtains x² and constant -10. Step 2 omits both cross products, reporting x²-10. Locate the first invalid step and correct it.