Simplify the expression (-x^4) - ((-2x)^4) as far as possible.

They also give this image with it I assume it's made to show it a little? I'm a little confused about it (via url, sorry, hard to explain without it I assume):

ibb.co/r0N6HkF

1 answer

(-x^4) - ((-2x)^4)
= -x^4 - 16x^4
= -17x^4
I don't see what the image has to do with it, since you are not multiplying two binomials.

Note that since a^4-b^4 = (a^2-b^2)(a^2+b^2) = (a-b)(a+b)(a^2+b^2),
(-x)^4 - (-2x)^4
= ((-x)^2 - (-2x)^2)((-x)^2 + (-2x)^2)
= ((-x)-(-2x))((-x)+(-2x))((-x)^2 + (-2x)^2)
= (x)(-3x)(x^2+4x^2)
= -3x^2(5x^2)
= -15x^4
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