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A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: $(a-b)^2=a^2-2ab+b^2$
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$\left(1-2\cos\left(x\right)+\cos\left(x\right)^2\right)\left(\tan\left(x\right)^3-\sin\left(x\right)^3\right)$
Learn how to solve problems step by step online. Expand and simplify the trigonometric expression (1-cos(x))^2(tan(x)^3-sin(x)^3). A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: (a-b)^2=a^2-2ab+b^2. We can multiply the polynomials \left(1-2\cos\left(x\right)+\cos\left(x\right)^2\right)\left(\tan\left(x\right)^3-\sin\left(x\right)^3\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). Then, combine the four terms in a sum. Substitute the values of the products.