Math Doubts

Square of Sum of Two terms formula

Formula

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

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

The square of sum of two terms is equal to sum of squares of both terms and two times the product of them.

Introduction

The square of sum of two terms or the special product of two same sum basis binomials is popularly expressed in mathematical form as either ${(a+b)}^2$ or ${(x+y)}^2$ in mathematics.

If $a$ and $b$ are two terms, then the sum of them is a binomial and it is written as $a+b$. The multiplication of the binomial by itself is a special case. So, the special product of them is written as ${(a+b)}^2$. It is read as square of sum of two terms $a$ and $b$. Actually, this algebraic identity is used as a formula in mathematics. Therefore, it is simply called as $a$ plus $b$ whole square formula. Similarly, if $x$ and $y$ are used to represent the two terms, then the square of sum of two terms rule is written as ${(x+y)}^2$.

Use

The square of sum of two terms identity is used as a formula in mathematics in two cases.

  1. The product of two same sum basis binomials is expanded as sum of squares of the terms and twice the product of both terms.
  2. The summation of squares of two terms and two times the product of same terms is simplified as the square of sum of them.


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