Math Doubts

Sum of Two squares formula


$(1). \,\,\,$ $a^2+b^2$ $\,=\,$ ${(a+b)}^2-2ab$

$(2). \,\,\,$ $x^2+y^2$ $\,=\,$ ${(x+y)}^2-2xy$

The sum of two square terms is equal to twice their product subtracted from square of sum of them, is called the sum of two squares formula. It is also called as the sum of two square terms formula.


In mathematics, the sum of two square terms are appeared and It is essential to express it into equivalent form in some special cases. Hence, the sum of two squares is written as two times their product less than the square of their sum, according to square of sum of two terms formula.

The sum of two squares formula is written generally in two ways and they are $a^2+b^2$ or $x^2+y^2$.

Other forms

The sum of two square terms formula can be written in terms any two terms.

$(1). \,\,\,$ $p^2+q^2$ $\,=\,$ ${(p+q)}^2-2pq$

$(2). \,\,\,$ $\alpha^2+\beta^2$ $\,=\,$ ${(\alpha+\beta)}^2-2\alpha\beta$

$(3). \,\,\,$ $\sin^2{\theta}+\cos^2{\theta}$ $\,=\,$ ${(\sin{\theta}+\cos{\theta})}^2-2\sin{\theta}\cos{\theta}$

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