Factor 192y^3+81z^3

Math
192y3+81z3
Factor 3 out of 192y3+81z3.
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Factor 3 out of 192y3.
3(64y3)+81z3
Factor 3 out of 81z3.
3(64y3)+3(27z3)
Factor 3 out of 3(64y3)+3(27z3).
3(64y3+27z3)
3(64y3+27z3)
Rewrite 64y3 as (4y)3.
3((4y)3+27z3)
Rewrite 27z3 as (3z)3.
3((4y)3+(3z)3)
Since both terms are perfect cubes, factor using the sum of cubes formula, a3+b3=(a+b)(a2-ab+b2) where a=4y and b=3z.
3((4y+3z)((4y)2-(4y)(3z)+(3z)2))
Factor.
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Simplify.
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Apply the product rule to 4y.
3((4y+3z)(42y2-(4y)(3z)+(3z)2))
Raise 4 to the power of 2.
3((4y+3z)(16y2-(4y)(3z)+(3z)2))
Multiply 4 by -1.
3((4y+3z)(16y2-4y(3z)+(3z)2))
Rewrite using the commutative property of multiplication.
3((4y+3z)(16y2-4⋅3yz+(3z)2))
Multiply -4 by 3.
3((4y+3z)(16y2-12yz+(3z)2))
Apply the product rule to 3z.
3((4y+3z)(16y2-12yz+32z2))
Raise 3 to the power of 2.
3((4y+3z)(16y2-12yz+9z2))
3((4y+3z)(16y2-12yz+9z2))
Remove unnecessary parentheses.
3(4y+3z)(16y2-12yz+9z2)
3(4y+3z)(16y2-12yz+9z2)
Factor 192y^3+81z^3

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