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Foil in reverse..
- x2 + qx + px + pq
- x2 + (p+q)x + pq
x2 + 9x + 8 = (x+p)(x+q) = x2 + (p+q)x + pq
We now list pairs of factors of 8 whose sum is 9.
- Pairs of factors_ 2, 4..doesnt work because their sum is 8.
- Pairs of factors_ 1, 8.. works because their sum is 9.
+ 9X + 8 = X2
+ 1X + 8X + 8
Factoring a difference of two squares
A2 - B2
(A + B)(A - B)
Factoring a sum or difference of two cubes
(A+B)(A2 - AB + B2)
A3 - B3
(A - B)(A2 + AB + B2)