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Hello everyone and thanks in advance for any help!
So I want to reduce Heron's formula to simplify equilateral triangles. But I'm getting caught up near the end:
Formula:
S=(a+b+c)/2, In this case S=3a/2 since a=b=c
A=(S(S-a)(S-a)(S-a))^1/2
So, ((3a/2)(3a/2-a)^3)^1/2
This is where I seem to lose it.
My calculator and wolfram agree that (3a/2)(3a/2-a)^3=(3a^4)/16
However, I am getting (57a^4)/16. I am cubing everything ((3^3a^3)/2^3-a^3) and multiplying that by 3a/2. I'm positive that my problem lays in cubing.
((3^3a^3)/2^3-a^3)=(27a^3)/8-a^3? wolfram claims a^3/8. I don't understand that at all! Where did that 3^3 go?? It has to be something simple that I'm missing or not doing correctly.
This emote: is definitely the most accurate representation of my current state.
Thanks for the help!