## ALGEBRAIC IDENTITIES

1. (a + b)

^{2}= a^{2}+ 2ab + b^{2}
2. (a − b)

^{2}= a^{2}− 2ab + b^{2}
3. (a + b)

^{2}+ (a − b)^{2}= 2(a^{2}+ b^{2})
4. (a + b)

^{2 }− (a − b)^{2 }= 4ab
5. (a + b)

^{3 }= a^{3}+ b^{3}+3ab (a+ b)
6. (a − b)

^{3}= a^{3}− b^{3}− 3ab (a − b)
7. (a

^{2}− b^{2}) = (a + b) (a − b)
8. (a

^{3}+ b^{3}) = (a + b) (a^{2}− ab + b^{2})
9. (a

^{3}− b^{3}) = (a − b) (a^{2}+b^{2}+ab)
10. (a
+ b+ c)

^{2}= a^{2}+ b^{2}+ c^{2}+2(ab + bc + ca)
11. (a
– b − c)

^{2}= a^{2}+ b^{2}+c^{2}− 2(ab + ac − bc)
12. (a
+ b + c)

^{3}= a^{3}+ b^{3}+ c^{3}+3(a+b) (b+c) (c+a)
13. (a

If a + b + c = 0 then, a^{3}+ b^{3}+ c^{3}– 3abc) = (a+b+c) (a^{2}+b^{2}+c^{2}− ab−bc −ca)^{3}+ b

^{3}+ c

^{3}= 3abc

####
15. x^{3}+y^{3}=(x+y) (x^{2}–xy+y^{2})

####
16. x^{3}–y^{3}=(x–y) (x^{2}+xy+y^{2})

####
17. x^{2}+y^{2}+z^{2}−xy–yz–zx=1/2[(x−y)^{2}+(y−z)^{2}+(z−x)^{2}]

1.

**Laws of Exponents**(a^{m})(a^{n}) = a^{m+n }(ab)^{m}= a^{m}b^{m }(a^{m})^{n}= a^{mn}
2.

**Fractional Exponents**
a.
a

^{0}= 1
b.
a

^{m}/a^{n}=a^{m}^{−}^{n}
c.
a

^{m}= 1/a^{−}^{m}
d.
a

^{−}^{m}= 1/a^{m}
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