To convert the expression (x+1)(x+3)(x-4) into standard form, you can first perform the multiplication and then simplify the resulting polynomial. Here's the step-by-step process:
1. Multiply the factors using the distributive property:
(x+1)(x+3)(x-4) = (x+1)(x^2 - 4x + 3x - 12)
2. Continue to simplify:
(x+1)(x^2 - 4x + 3x - 12) = (x+1)(x^2 - x - 12)
3. Apply the distributive property again:
(x+1)(x^2 - x - 12) = x(x^2 - x - 12) + 1(x^2 - x - 12)
4. Distribute x and 1 into the terms inside the parentheses:
x(x^2 - x - 12) + 1(x^2 - x - 12) = x^3 - x^2 - 12x + x^2 - x - 12
5. Combine like terms:
x^3 - 12x - 12
So, the expression (x+1)(x+3)(x-4) in standard form is:
x^3 - 12x - 12