Perfect Square Trinomials

Like the difference of squares formula, perfect square trinomial formulas are very common on the GRE.

${x}^{2}+2xy+{y}^{2}={\left(x+y\right)}^{2}$
${x}^{2}-2xy+{y}^{2}={\left(x-y\right)}^{2}$

For example, x2 + 6x + 9 = x2 + 2(3x)+ 32 =(x + 3)2 . Note, in a perfect square trinomial, the middle term is twice the product of the square roots of the outer terms.

Example: If r2 - 2rs+ s2 = 4 , then ( r - s)6 =

(A) - 4
(B) 4
(C) 8
(D) 16
(E) 64

r 2 - 2rs+ s2 = 4

by the formula x2 - 2xy+ y2 =(x - y)2
(r - s)2 = 4

by cubing both sides of the equation
[(r - s)2]3 = 43

by the rule (x a)b = x ab
(r - s)6 = 64

The answer is (E).