Question

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

Answer 1

`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!