Quanto é (2x-y)×(2x+y)×(x-y)
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Dada a propriedade:
= = = = =
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![\mathsf{=\left(2x-y\right)\cdot \left(2x+y\right)\cdot \left(x-y\right)}\\\\\mathsf{=\left[\left(2x-y\right)\cdot \:\left(2x+y\right)\right]\cdot \left(x-y\right)}\\\\\mathsf{=\left[\left(2x\right)^2-y^2\right]\cdot \left(x-y\right)}\\\\\mathsf{=\left(4x^2-y^2\right)\cdot \left(x-y\right)}\\\\\mathsf{=\left(4x^2\cdot x\right)-\left(4x^2\cdot y\right)-\left(y^2\cdot x\right)+\left(y^2\cdot y\right)}\\\\\boxed{\mathsf{=4x^3-4x^2y-xy^2+y^3}}\: \: \checkmark](https://tex.z-dn.net/?f=%5Cmathsf%7B%3D%5Cleft%282x-y%5Cright%29%5Ccdot+%5Cleft%282x%2By%5Cright%29%5Ccdot+%5Cleft%28x-y%5Cright%29%7D%5C%5C%5C%5C%5Cmathsf%7B%3D%5Cleft%5B%5Cleft%282x-y%5Cright%29%5Ccdot+%5C%3A%5Cleft%282x%2By%5Cright%29%5Cright%5D%5Ccdot+%5Cleft%28x-y%5Cright%29%7D%5C%5C%5C%5C%5Cmathsf%7B%3D%5Cleft%5B%5Cleft%282x%5Cright%29%5E2-y%5E2%5Cright%5D%5Ccdot+%5Cleft%28x-y%5Cright%29%7D%5C%5C%5C%5C%5Cmathsf%7B%3D%5Cleft%284x%5E2-y%5E2%5Cright%29%5Ccdot+%5Cleft%28x-y%5Cright%29%7D%5C%5C%5C%5C%5Cmathsf%7B%3D%5Cleft%284x%5E2%5Ccdot+x%5Cright%29-%5Cleft%284x%5E2%5Ccdot+y%5Cright%29-%5Cleft%28y%5E2%5Ccdot+x%5Cright%29%2B%5Cleft%28y%5E2%5Ccdot+y%5Cright%29%7D%5C%5C%5C%5C%5Cboxed%7B%5Cmathsf%7B%3D4x%5E3-4x%5E2y-xy%5E2%2By%5E3%7D%7D%5C%3A+%5C%3A+%5Ccheckmark "\mathsf{=\left(2x-y\right)\cdot \left(2x+y\right)\cdot \left(x-y\right)}\\\\\mathsf{=\left[\left(2x-y\right)\cdot \:\left(2x+y\right)\right]\cdot \left(x-y\right)}\\\\\mathsf{=\left[\left(2x\right)^2-y^2\right]\cdot \left(x-y\right)}\\\\\mathsf{=\left(4x^2-y^2\right)\cdot \left(x-y\right)}\\\\\mathsf{=\left(4x^2\cdot x\right)-\left(4x^2\cdot y\right)-\left(y^2\cdot x\right)+\left(y^2\cdot y\right)}\\\\\boxed{\mathsf{=4x^3-4x^2y-xy^2+y^3}}\: \: \checkmark")
= = = = =
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