Factor 729s^3b^6-125

Math
729s3b6-125
Rewrite 729s3b6 as (9sb2)3.
(9sb2)3-125
Rewrite 125 as 53.
(9sb2)3-53
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=9sb2 and b=5.
(9sb2-5)((9sb2)2+9sb2⋅5+52)
Simplify.
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Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to 9sb2.
(9sb2-5)((9s)2(b2)2+9sb2⋅5+52)
Apply the product rule to 9s.
(9sb2-5)(92s2(b2)2+9sb2⋅5+52)
(9sb2-5)(92s2(b2)2+9sb2⋅5+52)
Raise 9 to the power of 2.
(9sb2-5)(81s2(b2)2+9sb2⋅5+52)
Multiply the exponents in (b2)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(9sb2-5)(81s2b2⋅2+9sb2⋅5+52)
Multiply 2 by 2.
(9sb2-5)(81s2b4+9sb2⋅5+52)
(9sb2-5)(81s2b4+9sb2⋅5+52)
Multiply 5 by 9.
(9sb2-5)(81s2b4+45sb2+52)
Raise 5 to the power of 2.
(9sb2-5)(81s2b4+45sb2+25)
(9sb2-5)(81s2b4+45sb2+25)
Factor 729s^3b^6-125

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