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\left(4x^{2}+4x+1\right)\left(2x-1\right)^{3}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.
\left(4x^{2}+4x+1\right)\left(8x^{3}-12x^{2}+6x-1\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2x-1\right)^{3}.
32x^{5}-16x^{4}-16x^{3}+8x^{2}+2x-1
Use the distributive property to multiply 4x^{2}+4x+1 by 8x^{3}-12x^{2}+6x-1 and combine like terms.
\left(4x^{2}+4x+1\right)\left(2x-1\right)^{3}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.
\left(4x^{2}+4x+1\right)\left(8x^{3}-12x^{2}+6x-1\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2x-1\right)^{3}.
32x^{5}-16x^{4}-16x^{3}+8x^{2}+2x-1
Use the distributive property to multiply 4x^{2}+4x+1 by 8x^{3}-12x^{2}+6x-1 and combine like terms.