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

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Answer 1 · 2018-04-04T16:25:06

#2x^2 - 8x - 33#

Here's how I did it:

#(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!