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Answer:
1 for the first blank and
[tex]9b^2[/tex] for the second blank.
Step-by-step explanation:
By observation 27b³-1 is a perfect cube
27b³ = (3b)³
1 = 1³
Operation used is " - "
Therefore the problem is all about the difference of perfect cubes
Where:
[tex]a^3 - b^3 = (a - b)(a^2 + ab + b^2)[/tex]
Solving:
a = 3b
b = 1
Substituting the value of a and b
[tex]27b^3 - 1^3 = (3b - 1)((3b)^2 + 3b(1) + 1^2) \\27b^3 - 1^3 = (3b - 1)(9b^2 + 3b + 1^2)[/tex]
Therefore the answer is
1 for the first blank and
[tex]9b^2[/tex] for the second blank.
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