# សមភាពគួរកត់សំគាល់

ខាងក្រោមនេះជាសមភាពគួរកត់សំគាល់មួយចំនួនដែលគេប្រើញឹកញាប់នៅក្នុងគណិតវិទ្យា៖ ចំពោះគ្រប់ចំនួនពិត a និង b គេបាន៖

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

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

• ${\displaystyle (a+b)^{4}=a^{4}+4a^{3}b+6a^{2}b^{2}+4ab^{3}+b^{4}\,}$
• ${\displaystyle (a-b)^{4}=a^{4}-4a^{3}b+6a^{2}b^{2}-4ab^{3}+b^{4}\,}$
• ${\displaystyle a^{4}+b^{4}=(a^{2}+ab{\sqrt {2}}+b^{2})(a^{2}-ab{\sqrt {2}}+b^{2})\,}$
• ${\displaystyle a^{4}-b^{4}=(a-b)(a+b)(a^{2}+b^{2})\,}$

• ${\displaystyle (a+b)^{5}=a^{5}+5a^{4}b+10a^{3}b^{2}+10a^{2}b^{3}+5ab^{4}+b^{5}\,}$
• ${\displaystyle (a-b)^{5}=a^{5}-5a^{4}b+10a^{3}b^{2}-10a^{2}b^{3}+5ab^{4}-b^{5}\,}$
• ${\displaystyle a^{5}+b^{5}=(a+b)(a^{4}-a^{3}b+a^{2}b^{2}-ab^{3}+b^{4})\,}$
• ${\displaystyle a^{5}-b^{5}=(a-b)(a^{4}+a^{3}b+a^{2}b^{2}+ab^{3}+b^{4})\,}$

• ${\displaystyle a^{6}+b^{6}=(a^{2}+b^{2})(a^{4}-a^{2}b^{2}+b^{4})\,}$
• ${\displaystyle a^{6}-b^{6}=(a+b)(a-b)(a^{2}+ab+b^{2})(a^{2}-ab+b^{2})\,}$

• ${\displaystyle a^{7}+b^{7}=(a+b)(a^{6}-ab^{5}+a^{2}b^{4}-a^{3}b^{3}+a^{4}b^{2}-a^{5}b+b^{6})\,}$
• ${\displaystyle a^{7}-b^{7}=(a-b)(a^{6}+ab^{5}+a^{2}b^{4}+a^{3}b^{3}+a^{4}b^{2}+a^{5}b+b^{6})\,}$