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16\left(x^{5}\right)^{2}-16x^{5}x+4x^{2}-9\left(4x^{5}-2x\right)-1
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x^{5}-2x\right)^{2}.
16x^{10}-16x^{5}x+4x^{2}-9\left(4x^{5}-2x\right)-1
To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.
16x^{10}-16x^{6}+4x^{2}-9\left(4x^{5}-2x\right)-1
To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.
16x^{10}-16x^{6}+4x^{2}-36x^{5}+18x-1
Use the distributive property to multiply -9 by 4x^{5}-2x.
16\left(x^{5}\right)^{2}-16x^{5}x+4x^{2}-9\left(4x^{5}-2x\right)-1
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x^{5}-2x\right)^{2}.
16x^{10}-16x^{5}x+4x^{2}-9\left(4x^{5}-2x\right)-1
To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.
16x^{10}-16x^{6}+4x^{2}-9\left(4x^{5}-2x\right)-1
To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.
16x^{10}-16x^{6}+4x^{2}-36x^{5}+18x-1
Use the distributive property to multiply -9 by 4x^{5}-2x.