### Algebra: Notable Products

### The difference of two squares

Difference of two squares

With the difference between two squares, we can factorize with the following rule: \[\blue a^2-\green b^2=(\blue a+\green b) (\blue a-\green b)\] |
\[\begin{array}{rcl} x^2-16&=& \blue{x}^2-\green{4}^2 \\ &=& (\blue{x}+\green{4}) (\blue{x}-\green{4}) |

We can also use this formula, the other way around, to eliminate brackets: \[(\blue a+\green b) (\blue a-\green b) = \blue a^2-\green b^2\] |
\[\begin{array}{rcl} (\blue{x}+\green{5}) (\blue{x}-\green{5}) &=& \blue{x}^2-\green{5}^2 \\ &=& x^2-25 \\ |

#(2x+7)(2x-7)#

#\begin{array}{rcl}{4}{x}^2-49&=&(2x)^2-7^2\\&&\phantom{xxx}\blue{\text{recognize the square}}\\&=&(2x+7)(2x-7)\\&&\phantom{xxx}\blue{\text{factorize}}\end{array}#

#\begin{array}{rcl}{4}{x}^2-49&=&(2x)^2-7^2\\&&\phantom{xxx}\blue{\text{recognize the square}}\\&=&(2x+7)(2x-7)\\&&\phantom{xxx}\blue{\text{factorize}}\end{array}#

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