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We can multiply the polynomials $\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{y}-\sqrt{x}\right)$ 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 ($L\times L$)
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$\begin{matrix}(F\times F)\:=\:(\sqrt{x})(\sqrt{y})\\(O\times O)\:=\:(\sqrt{x})(-\sqrt{x})\\(I\times I)\:=\:(\sqrt{y})(\sqrt{y})\\(L\times L)\:=\:(\sqrt{y})(-\sqrt{x})\end{matrix}$
Learn how to solve special products problems step by step online. Solve the product (x^1/2+y^1/2)(y^1/2-x^1/2). We can multiply the polynomials \left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{y}-\sqrt{x}\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. When multiplying exponents with same base we can add the exponents.