# $(x+a)(x+b)$ formula

## Formula

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

$a$ and $b$ are constants and $x$ is a variable. $x+a$ and $x+b$ are two binomials in which $x$ is a common term but the second term is different. The product of such binomials is represented by $(x+a)(x+b)$ identity in algebra. It is mainly used to expand in terms of $x$, $a$ and $b$.

### Proof

The expansion of special product of binomials $x+a$ and $x+b$ can be proved in mathematics in two different methods.

#### Algebraic Method

The expansion of $(x+a)(x+b)$ identity is derived in algebra by the multiplication of algebraic expressions.

#### Geometrical Method

The expansion of $(x+a)(x+b)$ formula can also be derived geometrically by the areas of rectangle and square.