Expand and simplify. Express equations in standard form.
1. f(x) = -2(x-1)(x+4)(x+1)(x-3)
2. f(x) = (x+2)(x+1)(x+4)
3.f(x) = x(x-6)
consider these general forms
$\displaystyle a(b+c) =ab+ac $
$\displaystyle (a+b)(c+d) =ac+ad+bc+bd $
$\displaystyle (a+b)(c+d)(e+f) =eac+ead+ebc+ebd+fac+fad+fbc+fbd$
$\displaystyle (a+b)(c+d)(e+f)(g+h) $
$\displaystyle =geac+gead+gebc+gebd+gfac+gfad+gfbc+gfbd$
$\displaystyle +heac+head+hebc+hebd+hfac+hfad+hfbc+hfbd$
You must group like terms.
For this one, note first that (x - 1)(x + 1) = x^2 - 1. Then multiply this by the product of the other two linear factors, x^2 + x - 12. Multiply that through by the -2, and you're done.
You can multiply the polynomial factors in any order you like, but it might be quickest to multiply the x + 2 by the x + 4, and then multiply the result by the x + 1.
Take the x through the parentheses, and you're done.