Evaluate
8\left(a-2b\right)^{2}+4b-2a-1
Expand
8a^{2}-32ab-2a+32b^{2}+4b-1
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8\left(a^{2}-4ab+4b^{2}\right)-2a+4b-1
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-2b\right)^{2}.
8a^{2}-32ab+32b^{2}-2a+4b-1
Use the distributive property to multiply 8 by a^{2}-4ab+4b^{2}.
8\left(a^{2}-4ab+4b^{2}\right)-2a+4b-1
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-2b\right)^{2}.
8a^{2}-32ab+32b^{2}-2a+4b-1
Use the distributive property to multiply 8 by a^{2}-4ab+4b^{2}.
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