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

$x$ is a variable, $a$ and $b$ are two constants. The sum of literals $x$ and $a$ formed a binomial $x+a$, and difference of the literals $x$ and $b$ formed another binomial $x-b$. The first term of both multinomials is same. So, they are special binomials. Therefore, the product of them can be called as the special binomials product and it is written in mathematical form as follows.

$(x+a)(x-b)$

The product of the special polynomials $x+a$ and $x-b$ is equal to an algebraic expression $x^2+(a-b)x-ab$. This algebraic expression is used as expansion of the special binomial product $(x+a)(x-b)$ in algebraic mathematics.

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

This rule is actually used as a formula in mathematics if two opposite sign binomials contains one same variable, involved in multiplication.

$(l+4)(l-7)$ $\,=\,$ $l^2+(4-7)l-(4 \times 7)$

$\implies$ $(l+4)(l-7)$ $\,=\,$ $l^2-3l-28$

In fact, the product of special binomials can also obtained by the multiplication of algebraic expressions but it takes more time than using this formula. Hence, the expansion of $(x+a)(x-b)$ identity is used as formula to get their product quickly in mathematics.

The expansion of $(x+a)(x-b)$ can be derived in mathematical form in two different methods.

Learn how to derive the expansion of special binomials product $(x+a)(x-b)$ by multiplying the binomials $x+a$ and $x-b$.

Learn how to derive the expansion of special product of binomials $(x+a)$ and $(x-b)$ by the areas of rectangle and square.

Latest Math Topics

Mar 21, 2023

Feb 25, 2023

Feb 17, 2023

Feb 10, 2023

Jan 15, 2023

Latest Math Problems

Mar 03, 2023

Mar 01, 2023

Feb 27, 2023

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the math problems in different methods with understandable steps and worksheets on every concept for your practice.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved