[squaring binomials][section 38]

(1.)  (a + 3)2                here is the problem

=  (a + 3)(a + 3)          write it out

=   a2 + 3a + 3a + 9      foil multiply

=   a2 + 6a + 9             combine like terms

result:  a2 + 6a + 9

(2.)  (x - 2)2                 here is the problem

=  (x - 2)(x - 2)         write it out

=   x2 - 2x - 2x + 4      foil multiply

=   x2 - 4x + 4                combine like terms

result:  x2 - 4x = 4

(3.)  (2a + 1)2                  here is the problem

=   (2a + 1)(2a + 1)          write it out

=     4a2 + 2a + 2a + 1         foil multiply

=     4a2 + 4a + 1           combine like terms

result:  4a2 + 4a + 1

(4.)  (4a - 1)2                  here is the problem

=   (4a - 1)(4a - 1)        write it out

=    16a2 - 4a - 4a + 1      foil multiply

=   16a2 - 8a + 1    combine like terms

result:  16a2 - 8a + 1

(5.)  (3x - y)2                    here is the problem

=  (3x - y)(3x - y)          write it out

=     9x2 - 3xy - 3xy + y2    foil multiply

=    9x2 - 6xy + y2           combine like terms

result:  9x2 - 6xy + y2

(6.)  (2x + y)2                here is the problem

=    4x2 + 4xy + y2        square the binomial

result:  4x2 + 4xy + y2

(7.)  (5c + 3d)2                  here is the problem

=    25c2 + 30cd + 9d2       square the binomial

result:  25c2 + 30cd + 9d2

(8.)  (2a2 + 3)2                here is the problem

=     4a4 + 12a2 + 9          square the binomial

result:  4a4 + 12a2 + 9

(9.)  (2x - 3y)2                  here is the problem

=     4x2 - 12xy + 9y2       square the binomial

result:  4x2 - 12xy + 9y2

(10.)  (11a2 + c2)2               here is the problem

=     121a4 + 22a2c2 + c4      square the binomial

result: 121a4 + 22a2c2 + c4