[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