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]]. However, due to [[matrices]] not being commutative under multiplication, this identity doesn't hold for matrices. |
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==See Also== | ==See Also== | ||
| − | * [[Sum and | + | * [[Sum and difference of powers]] |
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{{stub}} | {{stub}} | ||
| + | [[Category:Algebra]] | ||
Latest revision as of 00:27, 25 January 2023
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. However, due to matrices not being commutative under multiplication, this identity doesn't hold for matrices.
See Also
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