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

Jun 13, 2017

${x}^{2} - 11 x + 28$

#### 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.

$\left(x - 4\right) \left(x - 7\right)$

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 $- 7 x$.

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

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.

${x}^{2} - 7 x - 4 x + 28$
${x}^{2} - 11 x + 28$, which is your final answer!