Product formulas formulas

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Product formulas

Variables

a

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Real number

b

→

Real number

n

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Integer

1.

Square of difference

(a-b)^2=a^2-2ab+b^2

Example

Example 1:| $(a-2)^2 = a^2 - 2\cdot a \cdot 2 + 2^2 = a^2 - 4a + 4$ Example 2:| $A (3x-5y)^2 &= (3x)^2 - 2 \cdot 3x \cdot 5y + (5y)^2\\ &= 9x^2 - 30xy + 25y^2 A$

2.

Square of sum

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

3.

Cube of difference

(a-b)^3=a^3-3a^2b+3ab^2-b^3

4.

Cube of sum

(a+b)^3=a^3+3a^2b+3ab^2+b^3

5.

Fourth power of difference

(a-b)^4=a^4-4a^3b+6a^2b^2-4ab^3+b^4

6.

Fourth power of sum

(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4

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