How do you simplify #(x - 4)(x - 7)#?
We begin by doing something called FOIL in math, or "first, outside, inside, last". It is a mnemonic device to help you remember how to multiply binomials. So lets start by multiplying the first parts of each binomial.
The "firsts" of this binomial product are x and x, and their product is
Next is the outsides, which are x and -7. Their product is
Now for the insides, which are -4 and x. Their product is
Lastly, the lasts, which are -4 and -7 in this case. A negative times a negative is a positive, and 4 times 7 is 28, so their product is 28.
Now to add everything together.