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(A+B)^{2}
A^{2 }+ 2AB + B^{2}

(AB)^{2}
A^{2}  2AB +B^{2}


Foil in reverse..
(x+p)(x+q)
 x^{2 }+ qx + px + pq
 or
 x^{2} + (p+q)x + pq

Example
x^{2} + 9x + 8 = (x+p)(x+q) = x^{2} + (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.
X ^{2 }+ 9X + 8 = X ^{2} + 1X + 8X + 8

Factoring a difference of two squares
A^{2 } B^{2}
(A + B)(A  B)

Factoring a sum or difference of two cubes
A^{3}+B^{3
}^{ }
(A+B)(A^{2}  AB + B^{2})

A^{3}  B^{3}
(A  B)(A^{2} + AB + B^{2})

