Factoring a difference of squares

Question

1. Identify the factors of z²-64
2. Identify the factors of 100-49w²
3. Paul says r²+100 is a difference of squares and Peter says it is not. Who is right? Explain your answer.

Answer 1

A simple trick, if you have a²-b² = (a+b)(a-b)

1. z²-64 = (z+8)(z-8)
2. 100-49w² = (10 + 7w)(10-7w)
3. This is not the difference of squares. When placing this equation in the quadratic equation, specifically √b²-4ac there is a negative answer remaining. There, there is no real solution, and it can't be factored with real numbers. Plotting this produces a parabolic function with no x intercepts

Hope this helps!