how do you distribute (2x-6)(4x-9) and simplify?

Answer 1

It is a math method called FOIL. First, Outer, Inner and Last.

First multiply 2x and 4x. Those are the First terms of the binomials.

you should get 8x^2 [eight x squared]

then, multiply 2x and -9 [these are the OUTER terms, because they are closest to the beginning and ending.

you should get -18x

your problem should look like this so far: 8x^2-18x

next, is the inner terms. multiply -6 and 4x. that gives us -24x

lastly is the LAST terms, -6 and -9 [because they are the last terms of the binomials. that gives us 54 (positive).

now, this is what it should look like.
8x^2-18x-24x+54

to simplify, we simply combine like terms.

since -18x and -24x have the same term "x", we can combine them to get -42x.

Your final answer is: 8x^2-42x+54

Answer 2

FOIL

First terms
Outside terms
Inside terms
Last terms

First terms = 2x by 4x = 8x^2
Outside terms = 2x by -9 = -18x
Inside terms = -6 by 4x = -24x
Last terms = -6 by -9 = 54

8x^2 -18x - 24x + 54

8x^2 - 42x + 54

Answer 3

Multiply each term like 2x by the other terms in brackets
8x^2-18x-24x+54
8x^2-42x+54
To simplify, divide by the same number to get the lowest coefficients. I divided by 2
4x^2-21x+27