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The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: $(a+b)(a-b)=a^2-b^2$.
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$\left(2x+y\right)^2+\left(x-2y\right)^2-5\left(x^2-y^2\right)$
Learn how to solve simplification of algebraic expressions problems step by step online. Simplify the expression (2x+y)^2+(x-2y)^2-5(x+y)(x-y). The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. Expand \left(x-2y\right)^2. Expand the expression \left(2x+y\right)^2 using the square of a binomial. Take the square of the first term: 2x.