(x - 1)(x + 4)(x - 3) find the product of the binomials

x³ - 13x + 12

step-by-step explanation:

if you are familiar with the distributive property

a(b+c) = a·b + a·c

then you can apply this here with the binomials.

since multiplication over the real numbers is commutative, we can multiply these binomials in any order. suppose we want to focus on the product (x - 1)(x + 4)

using the distributive property, we can distribute (x - 1) into (x+4):

(x - 1)(x + 4) = x(x - 1)+ 4(x - 1)

and then we apply the distributive property again:

  = x² - x + 4x - 4

combining like terms -x and 4x, we get that

  = x² + 3x - 4

hence we have that (x - 1)(x + 4) = x² + 3x - 4. in this original product, this means that

  (x - 1)(x + 4)(x - 3) = (x² + 3x - 4)(x - 3)

now we can take (x - 3) to the front

  = (x - 3)(x² + 3x - 4)

and then distribute (x-3) inside

  = x²(x - 3) + 3x(x - 3) - 4(x - 3)

now distribute again

  = x³ - 3x² + 3x² - 9x - 4x + 12

and combine like terms to get a final answer of

  = x³ - 13x + 12

what's that