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

Latest Math Problems

Email subscription

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.