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

The expansion of special product of binomials $x+a$ and $x+b$ can be derived in algebraic method by the multiplication of algebraic expressions.

Multiply each term of first binomial with the second binomial to perform multiplication of algebraic expressions.

${(x+a)}{(x+b)}$ $\,=\,$ $x \times (x+b)$ $+$ $a \times (x+b)$

Now, multiply each term of the second binomial by its multiplying factor.

$=\,$ $x \times x$ $+$ $x \times b$ $+$ $a \times x$ $+$ $a \times b$

Now, write product of the terms in an order to obtain the special product of binomials $x+a$ and $x+b$.

$=\,$ $x^2$ $+$ $xb$ $+$ $ax$ $+$ $ab$

$=\,$ $x^2$ $+$ $bx$ $+$ $ax$ $+$ $ab$

$=\,$ $x^2$ $+$ $ax$ $+$ $bx$ $+$ $ab$

$x$ is a common multiplying factor in two terms of the expression. So, take it common from them to express the expansion of $(x+a)(x+b)$ formula in algebraically.

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

List of most recently solved mathematics problems.

Jul 04, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \,\to\, \tan^{-1}{3}} \normalsize {\dfrac{\tan^2{x}-2\tan{x}-3}{\tan^2{x}-4\tan{x}+3}}$

Jun 23, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \to 0} \normalsize \dfrac{e^{x^2}-\cos{x}}{x^2}$

Jun 22, 2018

Integral Calculus

Evaluate $\displaystyle \int \dfrac{1+\cos{4x}}{\cot{x}-\tan{x}} dx$

Jun 21, 2018

Limit

Evaluate $\displaystyle \large \lim_{x \to \infty} \normalsize {\sqrt{x^2+x+1}-\sqrt{x^2+1}}$

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.