**Perfect Square Trinomials**

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

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

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

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

For example, x

^{2}+ 6x + 9 = x

^{2}+ 2(3x)+ 3

^{2}=(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 *r*^{2} - 2*rs*+ *s*^{2} = 4 , then (* r - s*)^{6} =

(A) - 4

(B) 4

(C) 8

(D) 16

(E) 64

*r*

^{2}- 2

*rs*+

*s*

^{2}= 4

by the formula

*x*

^{2}- 2

*xy*+ y

^{2}=(

*x - y*)

^{2}

(r - s)

^{2}= 4

by cubing both sides of the equation

[(

*r - s*)

^{2}]

^{3}= 4

^{3}

by the rule (

*x*)

^{ a}*=*

^{b}*x*

^{ab}(

*r - s*)

^{6}= 64

The answer is (E).