[multiplying rational expressions][section 53]

(1.)  3x - 48y2       3x + 6y
___________ * ____________           here is the problem
2x2 - 8y2       3x + 12y

=    3(x - 16y2)             3(x + 2y)
_________________  *   _______________    factor
2(x2 - 4y2)              3(x + 4y)

=     3(x - 16y2)                3(x + 2y)
______________________  *  _______________
2(x - 2y)(x + 2y)        3(x + 4y)      factor

=        3(x - 16y2)
__________________________   cancel and multiply
2(x - 2y)(x + 4y)

(2.)  x2 + 8x + 16     x - 3
_____________ * ________          here is the problem
x2 - 9        x + 4

=   (x + 4)2                (x - 3)        factor
________________  *   ____________
(x - 3)(x + 3)         (x + 4)

=      (x + 4)
___________________          cancel and multiply
(x + 3)

(3.)    9 - x2           x
______  *   _________            here is the problem
x + 3         3 - x

=    (3 - x)(3 + x)             x
___________________  * _______________
(x + 3)           -(x - 3)        factor

=    -x                 cancel and multiply

(4.)     24x2                3x - 6
________________  *  _________         here is the problem
3(x2 - 4x + 4)          2x

=      24x2             3(x - 2)
_______________ *  ____________
3(x - 2)2            2x           factor

=    12x/(x - 2)         cancel and multiply

(5.)   5m + 5n        m2 - mn
_________  *  ____________      here is the problem
m2 - n2         (m + n)2

=     5(m + n)               m(m - n)
____________________  *  _______________
(m + n)(m - n)           (m + n)2          factor

=      5m/(m + n)2            cancel and multiply

(6.)    a2 + 6a + 5         5a - 15
_____________  * _______________   here is the problem
a - 3         a2 + 4a - 5

=    (a + 5)(a + 1)          5(a - 3)
__________________ *  ________________
(a - 3)          (a + 5)(a - 1)   factor

=      5(a + 1)/(a - 1)    cancel and multiply

(7.)   x2 - 3x - 18          3x + 3
________________ *  ______________   here is the problem
x2 - x - 2          x2 - 2x - 15

=    (x - 6)(x + 3)             3(x + 1)
___________________   *  ___________________
(x + 1)(x - 2)          (x - 5)(x + 3)      factor

=    3(x - 6)
_______________
(x - 2)(x - 5)     cancel and multiply

(8.)     4x2 - 9y2                    6xy     here is the problem
____________________  *  ________________
6x2 - 9xy                4xy + 6y2

=     (2x - 3y)(2x + 3y)               6xy
__________________________  *  __________________
3x(2x - 3y)                   2y(2x + 3y)  factor

=      1               cancel

(9.)   a2 + a - 2             a2 - 2a - 8     here is the problem
________________  *   ________________
a2 - 3a - 10          a2 - 7a + 12

=     (a + 2)(a - 1)           (a - 4)(a + 2)
______________________ *  _________________
(a - 5)(a + 2)          (a - 3)(a - 4)    factor

=    (a - 1)(a + 2)
_________________
(a - 5)(a - 3)         cancel and multiply

(10.)   c2 - 6c               c + 3
____________   *   ____________     here is the problem
c - 6                  c

=   c(c - 6)        (c + 3)
____________ *  ____________      factor
(c - 6)            c

=     c + 3               cancel and multiply