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The solution $a^2 - (b - 1)^2$ can be rewritten using the difference of squares as $\{a + (b - 1)\}\{ - (b - 1)\}$.
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To factor $(a^2)^2 + 2a^2 \times 8b^2 + (8b^2)^2$ into $(a^2 + 4ab + 8b^2)$, recognize it as a complete of a binomial.
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The formula for the difference of two squares is given by $a^2 - b^2 = $ ( + b)(a-b).
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To resolve $a^2 - 1 + 2b - b^2$ into factors, start by recognizing it as $a^2 - (b^2 - 2b + )$.
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In the factorization of $a^4 + 64b^4$, express it first as $(a^2)^2 + (8b^2)^2 - ab^2$.
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