The expansion of (x-a)(x-b) formula can be derived in algebraic approach by multiplying the two difference basis different binomials $x-a$ and $x-b$. According to multiplication of algebraic expressions, the special product of them can be obtained in mathematics.

Multiply the algebraic expressions $x-a$ and $x-b$ to express their product in mathematical form.by the multiplication of algebraic expressions.

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

According to the multiplication of algebraic expressions, multiply each term in the second polynomial by the each term in the first polynomial.

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

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

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

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

The expansion of the special product of the binomials can be further simplified for expressing 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 proved that the special product of the binomials $x-a$ and $x-b$ can be expanded as an algebraic expression $x^2-(a+b)x+ab$ in mathematics. In this way, the expansion of the special product of binomials $(x-a)(x-b)$ can be derived in algebra.

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