What you’ll learn
Factor difference of squares.
Key idea
Conjugate factors use opposite constant signs so their cross terms cancel.
Opposite signs cancel cross terms; squared differences and original expanded expressions do not satisfy the requested conjugate factor form.
Worked example
Enter the exact value or ordered values in the format requested below.
Factor x²-9 using conjugate binomials. Enter product, not original expansion.
- The subtracted quantities are squares x² and 3²=9.
- (x-3)(x+3) has opposite cross terms which cancel; constant product is -9, while repeating the negative factor creates middle coefficient -6.
Answer: (x-3)(x+3)
Quick Check
Evaluate a worked attempt at factor difference of squares, identify the first invalid step, and provide the correction.
Factor x²-196: Step 1 recognizes roots x and 14. Step 2 writes (x-14)(x-14). Locate the first invalid step and repair the product.