[perfect square trinomials][section 43]

(1.)  x2 + 6x + 9              here is the problem

=  (x + 3)(x + 3)              factor

=  (x + 3)2           use an exponent

(2.)    n2 + 14n + 49      here is the problem

=  (n + 7)(n + 7)          factor

=  (n + 7)2                 factor

(3.)    x2 - 10x + 25            here is the problem

=  (x - 5)(x - 5)               factor

=  (x - 5)2               use an exponent

(4.)  4x2 + 12xy + 9y2              here is the problem

=   (2x + 3y)(2x + 3y)          factor

=  (2x + 3y)2             use an exponent

(5.)   1 + 8x + 16x2           here is the problem

=   (1 + 4x)(1 + 4x)           factor

=   (1 + 4x)2              use an exponent

(6.)   4x2 - 4x + 1            here is the problem

=   (2x - 1)(2x - 1)           factor

=   (2x - 1)2       use an exponent

(7.)   1 - 6b + 9b2             here is the problem

=   (1 - 3b)(1 - 3b)                factor

=  (1 - 3b)2                use an exponent

(8.)   49a2 - 84a + 36          here is the problem

=   (7a - 6)(7a - 6)             factor

=   (7a - 6)2             use an exponent

(9.)  (a2 + 2ab + b2) - c2          here is the problem

=  (a + b)2 - c2                   factor

=  (a + b - c)(a + b + c)            factor

(10.)  4 - 20b + 25b2           here is the problem

=   (2 - 5b)(2 - 5b)             factor

=   (2 - 5b)2           use an exponent