Difference between revisions of "Difference of squares"
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Recognizing a '''difference of squares''' is a commonly used [[factoring]] technique in [[algebra]]. It refers to the identity <math>a^2 - b^2 = (a+b)(a-b)</math>. Note that this identity depends only on the (right and left) [[distributive property]] and the [[commutative property]] of multiplication and so holds not only for [[real]] or [[complex number]]s but also for [[polynomial]]s, in [[modular arithmetic | arithmetic modulo]] <math>m</math> for any [[positive integer]] <math>m</math>, or more generally in any [[commutative ring]]. | Recognizing a '''difference of squares''' is a commonly used [[factoring]] technique in [[algebra]]. It refers to the identity <math>a^2 - b^2 = (a+b)(a-b)</math>. Note that this identity depends only on the (right and left) [[distributive property]] and the [[commutative property]] of multiplication and so holds not only for [[real]] or [[complex number]]s but also for [[polynomial]]s, in [[modular arithmetic | arithmetic modulo]] <math>m</math> for any [[positive integer]] <math>m</math>, or more generally in any [[commutative ring]]. | ||
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==See Also== | ==See Also== | ||
* [[Sum and difference of powers]] | * [[Sum and difference of powers]] | ||
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{{stub}} | {{stub}} | ||
| + | [[Category:Algebra]] | ||
Revision as of 13:20, 14 July 2021
Recognizing a difference of squares is a commonly used factoring technique in algebra. It refers to the identity 
. Note that this identity depends only on the (right and left) distributive property and the commutative property of multiplication and so holds not only for real or complex numbers but also for polynomials, in arithmetic modulo 
for any positive integer , or more generally in any commutative ring.
See Also
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