Factor 81r^6+24r^3y^3

Math
81r6+24r3y3
Factor 3r3 out of 81r6+24r3y3.
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Factor 3r3 out of 81r6.
3r3(27r3)+24r3y3
Factor 3r3 out of 24r3y3.
3r3(27r3)+3r3(8y3)
Factor 3r3 out of 3r3(27r3)+3r3(8y3).
3r3(27r3+8y3)
3r3(27r3+8y3)
Rewrite 27r3 as (3r)3.
3r3((3r)3+8y3)
Rewrite 8y3 as (2y)3.
3r3((3r)3+(2y)3)
Since both terms are perfect cubes, factor using the sum of cubes formula, a3+b3=(a+b)(a2-ab+b2) where a=3r and b=2y.
3r3((3r+2y)((3r)2-(3r)(2y)+(2y)2))
Factor.
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Simplify.
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Apply the product rule to 3r.
3r3((3r+2y)(32r2-(3r)(2y)+(2y)2))
Raise 3 to the power of 2.
3r3((3r+2y)(9r2-(3r)(2y)+(2y)2))
Multiply 3 by -1.
3r3((3r+2y)(9r2-3r(2y)+(2y)2))
Rewrite using the commutative property of multiplication.
3r3((3r+2y)(9r2-3⋅2ry+(2y)2))
Multiply -3 by 2.
3r3((3r+2y)(9r2-6ry+(2y)2))
Apply the product rule to 2y.
3r3((3r+2y)(9r2-6ry+22y2))
Raise 2 to the power of 2.
3r3((3r+2y)(9r2-6ry+4y2))
3r3((3r+2y)(9r2-6ry+4y2))
Remove unnecessary parentheses.
3r3(3r+2y)(9r2-6ry+4y2)
3r3(3r+2y)(9r2-6ry+4y2)
Factor 81r^6+24r^3y^3

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