Math Doubts

Special Products of Binomials

The binomials are often involved in multiplication in some special forms and the products of such special form binomials are called as the special products of binomials. In mathematics, they are often used as formulas and it is very important to learn them for studying the algebra further. Here is the list of special products of binomials in algebraic form with proofs and examples.

Product of sum basis Binomials

$(1) \,\,\,$ ${(a+b)}^2$ $\,=\,$ $a^2+b^2+2ab$
$(2) \,\,\,$ ${(x+y)}^2$ $\,=\,$ $x^2+y^2+2xy$

Product of Difference basis Binomials

$(1) \,\,\,$ ${(a-b)}^2$ $\,=\,$ $a^2+b^2-2ab$
$(2) \,\,\,$ ${(x-y)}^2$ $\,=\,$ $x^2+y^2-2xy$

Product of Opposite sign Binomials

$(1) \,\,\,$ ${(a+b)}{(a-b)}$ $\,=\,$ $a^2-b^2$
$(2) \,\,\,$ ${(x+y)}{(x-y)}$ $\,=\,$ $x^2-y^2$

Product of Special case Binomials

$(1) \,\,\,$ ${(x+a)}{(x+b)}$ $\,=\,$ $x^2+(a+b)x+ab$

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

$(3) \,\,\,$ ${(x-a)}{(x+b)}$ $\,=\,$ $x^2-(a-b)x-ab$

$(4) \,\,\,$ ${(x-a)}{(x-b)}$ $\,=\,$ $x^2-(a+b)x+ab$

Math Doubts
Math Doubts is a free math tutor for helping students to learn mathematics online from basics to advanced scientific level for teachers to improve their teaching skill and for researchers to share their research projects. Know more
Follow us on Social Media
Math Problems

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.

Learn more