81r6+24r3y3

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))

Simplify.

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