How do you simplify #(x - 4)(x - 7)#?

1 Answer
Jun 13, 2017

Answer:

#x^2-11x+28#

Explanation:

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.

#(x-4)(x-7)#

The "firsts" of this binomial product are x and x, and their product is#x^2#.

Next is the outsides, which are x and -7. Their product is #-7x#.

Now for the insides, which are -4 and x. Their product is #-4x#.

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.

#x^2-7x-4x+28#

Simplifies to...

#x^2-11x+28#, which is your final answer!