Algebraic identities in Factor form

There are two useful algebraic identities in mathematics and they are used as formulas to factorize (or factorise) the difference of quantities with exponents. Now, let’s learn the algebraic identities in factor form with proofs and understandable arithmetic examples.

Difference of Squares

The difference of quantities in square form is equal to the product of their sum and difference. It is called the difference of squares property and it is written in algebraic form to use it as a formula in mathematics. The difference of squares identity is generally written in two popular forms as follows.

$(1).\,\,\,$ $a^2-b^2$ $\,=\,$ $(a+b)(a-b)$

$(2).\,\,\,$ $x^2-y^2$ $\,=\,$ $(x+y)(x-y)$

Difference of Cubes

The difference of quantities in cube form is equal to the product of the difference and the addition of the product of quantities and sum of their squares. It is called the difference of cubes property and it is written in algebraic form for using it as a formula in mathematics. The difference of cubes identity is popularly written in following two popular forms.

$(1).\,\,\,$ $a^3-b^3$ $\,=\,$ $(a-b)(a^2+b^2+ab)$

$(2).\,\,\,$ $x^3-y^3$ $\,=\,$ $(x-y)(x^2+y^2+xy)$

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