Problem: multiply (x+2)(3x-4)(2x+3)
(x + 2)(3x - 4)(2x + 3)
Begin with the first two sets of parentheses.
(x + 2)(3x - 4) (2x + 3) The separation is just to make
it easier to see where we are working.
(x + 2)(3x - 4) (2x + 3)
(3x^2 + 6x - 4x - 8) (2x + 3)
(3x^2 + 2x - 8) (2x + 3)
(3x^2 + 2x - 8)(2x + 3) Now use the third set of parentheses.
6x^3 + 4x^2 - 16x + 9x^2 + 6x - 24
6x^3 + 13x^2 - 10x - 24
Let's supply a value for x and see if this checks.
Let x = 5.
(x + 2)(3x - 4)(2x + 3) = 6x^3 + 13x^2 - 10x - 24
(5 + 2)(3(5) - 4)(2(5) + 3) = 6(5)^3 + 13(5)^2 - 10(5) - 24
(7)(15 - 4)(10 + 3) = 6(125) + 13(25) - 50 - 24
(7)(11)(13) = 750 + 325 - 50 - 24
1001 = 1001
Answer: (x+2)(3x-4)(2x+3) = 6x^3 + 13x^2 - 10x - 24