[multiplying polynomials][section 36]

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

=   2a2 + 3a          multiply thru parentheses

result:  2a2 + 3a

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

=   -2y2 - 12y         multiply thru parentheses

result:  -2y2 - 12y

(3.)  2a(a2 - 4a + 3)           here is the problem

=     2a3 - 8a2 + 6a         multiply thru parenthesews

result:  2a3 - 8a2 + 6a

(4.)   -3x(x2 + 5x + 2)           here is the problem

=   -3x3 - 15x2 - 6x         multiply thru parentheses

result:  -3x3 - 15x2 - 6x

(5.)  (a + 7)(a + 3)           here is the problem

=    a2 + 3a + 7a + 21        foil multiply

=    a2 + 10a + 21           combine like terms

result:  a2 + 10a + 21

(6.)  (x + 9)(x + 5)           here is the problem

=    x2 + 5x + 9x + 45      foil multiply

=    x2 + 14x + 45

result:  x2 + 14x + 45

(7.)  (2a + 3b)(a - b)        here is the problem

=   2a2 - 2ab + 3ab - 3b2         foil multiply

=   2a2 + ab - 3b2        combine like terms

result:  2a2 + ab - 3b2

(8.)   (a + b)(c - d)          here is the problem

=   ac - ad + bc - bd            foil multiply

result: ac - ad + bc - bd

(9.)   (a2 + b)(a2 - 2b)        here is the problem

=    a4 - 2a2b + a2b - 2b2    foil multiply

=   a4 - a2b - 2b2       combine like terms

result:  a4 - a2b - 2b2

(10.)  (y - 6)(2y + 8)       here is the problem

=      2y2 + 8y - 12y - 48    foil multiply

=     2y2 - 4y - 48             combine like terms

result: 2y2 - 4y - 48