Solve the equation $\left(a^2+b^2\right)\left(x^2+y^2\right)=\left(ax-by\right)^2+\left(bx+ay\right)^2$

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Final answer to the problem

true

Step-by-step Solution

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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: $(a-b)^2=a^2-2ab+b^2$

$\left(a^2+b^2\right)\left(x^2+y^2\right)=\left(ax\right)^2-2axby+\left(by\right)^2+\left(bx+ay\right)^2$

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$\left(a^2+b^2\right)\left(x^2+y^2\right)=\left(ax\right)^2-2axby+\left(by\right)^2+\left(bx+ay\right)^2$

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Learn how to solve equations problems step by step online. Solve the equation (a^2+b^2)(x^2+y^2)=(ax-by)^2+(bx+ay)^2. 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. The power of a product is equal to the product of it's factors raised to the same power. Move everything to the left hand side of the equation. Multiply the single term x^2+y^2 by each term of the polynomial \left(a^2+b^2\right).

Final answer to the problem

true

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Main Topic: Equations

In mathematics, an equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions.

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