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Expand $\left(-3x^2-x^{-1}\right)^2$
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$\left(3x^2-3x\right)^3\left(\left(-3x^2\right)^2+6x^2x^{-1}+x^{-2}\right)$
Learn how to solve definition of derivative problems step by step online. Expand the expression (3x^2-3x)^3(-3x^2-x^(-1))^2. Expand \left(-3x^2-x^{-1}\right)^2. When multiplying exponents with same base we can add the exponents. The cube of a binomial (difference) is equal to the cube of the first term, minus three times the square of the first by the second, plus three times the first by the square of the second, minus the cube of the second term. In other words: (a-b)^3=a^3-3a^2b+3ab^2-b^3 = (3x^2)^3+3(3x^2)^2(-3x)+3(3x^2)(-3x)^2+(-3x)^3 =. We can multiply the polynomials \left(\left(3x^2\right)^3-9\left(3x^2\right)^2x+9x^2\left(-3x\right)^2+\left(-3x\right)^3\right)\left(\left(-3x^2\right)^2+6x+x^{-2}\right) by using the FOIL method. The acronym F O I L stands for multiplying the terms in each bracket in the following order: First by First (F\times F), Outer by Outer (O\times O), Inner by Inner (I\times I), Last by Last (L\times L).