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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

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

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

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

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