(-6+3ab)*((9*a^(2)*b^(2))-36)*(6-3ab)

asked by guest
on Nov 17, 2024 at 2:11 pm



You asked:

Evaluate the expression: \(\left(-6 + 3 a b\right) \cdot \left(9 \cdot {a}^{2} \cdot {b}^{2} - 36\right) \cdot \left(6 - 3 a b\right)\)

MathBot Answer:

Evaluated



\(\displaystyle \left(-6 + 3 a b\right) \cdot \left(9 \cdot {a}^{2} \cdot {b}^{2} - 36\right) \cdot \left(6 - 3 a b\right) = \left(9 a^{2} b^{2} - 36\right) \left(- 3 a b + 6\right) \left(3 a b - 6\right) \)

Expanded

\[\left(-6 + 3 a b\right) \cdot \left(9 \cdot {a}^{2} \cdot {b}^{2} - 36\right) \cdot \left(6 - 3 a b\right) = - 81 a^{4} b^{4} + 324 a^{3} b^{3} - 1296 a b + 1296\]

Factored

\[\left(-6 + 3 a b\right) \cdot \left(9 \cdot {a}^{2} \cdot {b}^{2} - 36\right) \cdot \left(6 - 3 a b\right) = - 81 \left(a b - 2\right)^{3} \left(a b + 2\right)\]

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