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

$a$ and $b$ are two constants, and $x$ is a variable. The literals $x$ and $a$ formed a binomial $x-a$ by their difference. Similarly, the literals $x$ and $b$ also formed another binomial $x-b$ by their difference. The two polynomials are called as special binomials because the first term in each expression is same.

Hence, the product of them is called as the special product of binomials. It is written in the following mathematical form algebraically.

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

The product of them is equal to an algebraic expression $x^2-(a+b)x+ab$. Therefore, the product of special binomials $x-a$ and $x-b$ is expanded as $x^2-(a+b)x+ab$ in algebraic mathematics.

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

This rule is used as a formula in mathematics when two difference basis binomials are involved in multiplication and a term in both polynomials is same.

$(p-3)(p-5)$ $\,=\,$ $p^2-(3+5)p+(3 \times 5)$

$\implies$ $(p-3)(p-5)$ $\,=\,$ $p^2-8p+15$

Actually, the product $(p-3)(p-5)$ can be obtained as per multiplication of algebraic expressions but it is a time taking process. Therefore, the algebraic identity is used as a formula in mathematics for obtaining the product of two difference basis special binomials in only two steps.

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

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

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

Latest Math Topics

Aug 31, 2024

Aug 07, 2024

Jul 24, 2024

Dec 13, 2023

Latest Math Problems

Sep 04, 2024

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved