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To verify $54ay^2 = 3 \cdot (2a) \cdot (3y)^2$, the square term in the factorization is $$
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For the expression $27y^3 = (3y)^3$, the base expression being cubed is $$
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The factorized form of $8a^3 + 36a^2y + 54ay^2 + 27y^3$ is $$
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If $36a^2y = 3 \cdot (2a)^2 \cdot $, then it matches the middle term of the sum of cubes.
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The expression $8a^3 + 36a^2y + 54ay^2 + 27y^3$ can be identified as a perfect cube because it fits the form of $$ cubes.
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