The product of binomials $x+a$ and $x-b$ is $(x+a)(x-b)$ and the expansion of the special product can be derived in algebraic method. The expansion of (x+a)(x-b) formula is actually derived by multiplying the algebraic expressions $x+a$ and $x-b$.

Multiply the algebraic expressions $x+a$ and $x-b$ for expressing the product of them in mathematical form by multiplying the algebraic expressions.

$(x+a) \times (x-b)$ $\,=\,$ $(x+a)(x-b)$

$\implies$ $(x+a)(x-b)$ $\,=\,$ $(x+a) \times (x-b)$

As per the multiplication of algebraic expressions, multiply each term of the second polynomial by the each term of the first polynomial.

$\implies$ $(x+a)(x-b)$ $\,=\,$ $x(x-b)+a(x-b)$

$\implies$ $(x+a)(x-b)$ $\,=\,$ $x \times x$ $+$ $x \times (-b)$ $+$ $a \times x$ $+a \times (-b)$

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

In this way, the special product of the multinomials $x+a$ and $x-b$ is expanded as an algebraic expression $x^2-xb+ax-ab$.

Now, the expansion of the special product of the binomials is simplified further to write it in simple form.

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

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

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

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

Therefore, it is successfully proved that the special product of the binomials $x+a$ and $x-b$ is expanded as an algebraic expression $x^2+(a-b)x-ab$ in mathematics. Thus, the expansion of the special product of the binomials $(x+a)(x-b)$ is derived algebraically in algebraic mathematics.

Latest Math Topics

Apr 18, 2022

Apr 14, 2022

Apr 05, 2022

Mar 18, 2022

Mar 05, 2022

Latest Math Problems

Apr 06, 2022

Mar 22, 2022

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 maths problems in different methods with understandable steps.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved