How do you multiply ( x + 7 ) ( x − 4 ) ( x − 7 ) ( x − 4 ) ?

1 Answer
Apr 4, 2018

2x^2 - 8x - 33

Here's how I did it:

Explanation:

(x+7)(x-4)(x-7)(x-4)

It's easier to solve it when we look at it like this instead:
(x+7)(x-7)(x-4)(x-4)


First, let's do the (x+7)(x-7) part:
x * x = x^2

x * -7 = -7x

7 * x = 7x

7 * -7 = -49

When we combine it all together, we get:
x^2 - 7x + 7x - 49

And we can simplify that to get:
x^2 - 49


Now let's do the (x-4)(x-4) part:
x * x = x^2

x * -4 = -4x

-4 * x = -4x

-4 * -4 = 16

When we combine it all together, we get:
x^2 - 4x - 4x + 16

And we can simplify that to get:
x^2 - 8x + 16


And when we combine everything together, we get:
x^2 - 49 + x^2 - 8x + 16

We can simplify this to get:
2x^2 - 8x - 33

Hope this helps!