Evaluate
\left(x^{2}-4\right)^{3}
Expand
x^{6}-12x^{4}+48x^{2}-64
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\left(x^{3}+6x^{2}+12x+8\right)\left(x-2\right)^{3}
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+2\right)^{3}.
\left(x^{3}+6x^{2}+12x+8\right)\left(x^{3}-6x^{2}+12x-8\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-2\right)^{3}.
x^{6}-12x^{4}+48x^{2}-64
Use the distributive property to multiply x^{3}+6x^{2}+12x+8 by x^{3}-6x^{2}+12x-8 and combine like terms.
\left(x^{3}+6x^{2}+12x+8\right)\left(x-2\right)^{3}
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+2\right)^{3}.
\left(x^{3}+6x^{2}+12x+8\right)\left(x^{3}-6x^{2}+12x-8\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-2\right)^{3}.
x^{6}-12x^{4}+48x^{2}-64
Use the distributive property to multiply x^{3}+6x^{2}+12x+8 by x^{3}-6x^{2}+12x-8 and combine like terms.
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