For Reiny:What step did I do wrong.(Help)
(x-4x^3)^2
=(x-4x^3)(x-4x^3)=(x)(x)+(x)(-4x^3)+(-4x^3)(x)+(-4x^3)(4x^3)
= x^2-4x^4-4x^4-16x^6
=x^2-8x^4-16x^6
Your answer is correct. You did nothing wrong.
-16x^2=>+16x^2
should have looked a bit more carefully
the last term should be + 16x^6
(in your second line: should have been
=(x-4x^3)(x-4x^3)=(x)(x)+(x)(-4x^3)+(-4x^3)(x)+(-4x^3)(-4x^3)
Thanks Reiny, Thanks Anonymous I went over it and found the problem.
To find the step you did wrong, let's start from the beginning and simplify the expression correctly.
Starting with (x-4x^3)^2, you correctly expanded it using the FOIL method as (x)(x)+(x)(-4x^3)+(-4x^3)(x)+(-4x^3)(-4x^3).
However, there is a mistake in the next step where you combined the terms. Let's go through it step by step:
(x)(x) = x^2
(x)(-4x^3) = -4x^4
(-4x^3)(x) = -4x^4 (note that this term is the same as the previous one)
(-4x^3)(-4x^3) = +16x^6 (multiplying two negative signs gives a positive)
Now, let's combine the like terms:
x^2 - 4x^4 - 4x^4 + 16x^6
Combining the -4x^4 terms, we get:
x^2 - 8x^4 + 16x^6
So the correct expression after expanding and simplifying is x^2 - 8x^4 + 16x^6.
It seems that you made a mistake while combining the -4x^4 terms. Make sure to double-check your signs and carefully combine like terms when simplifying algebraic expressions.