# Short multiplication formulas

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## Square of sum:

(a + b)^{2}
= a^{2}
+
2ab
+ b^{2}

## Square of difference:

(a − b)^{2}
= a^{2}
−
2ab
+ b^{2}

## Cube of sum:

(a + b)^{3}
= a^{3}
+
3a^{2}b
+
3b^{2}a
+ b^{3}

## Cube of difference:

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

## Binomal theorem:

(a + b)^{n}
= C_{0}^{n}a^{n}
+
C_{1}^{n}a^{n−1}b
+ ... +
C_{k}^{n}a^{n−k}b^{k}
+
C_{n}^{n}b^{n}
, coefficients
C_{k}^{n}
= n! / [k!(n − k)!]

## Sum of squares:

a^{2} + b^{2}
- not expands

## Difference of squares:

a^{2} − b^{2}
= (a − b)(a + b)

## Sum of cubes:

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

## Difference of cubes:

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