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 \\ |
#(18b+7)(18b-7)#
#\begin{array}{rcl}{324}{b}^2-49&=&(18b)^2-7^2\\&&\phantom{xxx}\blue{\text{recognize the square}}\\&=&(18b+7)(18b-7)\\&&\phantom{xxx}\blue{\text{factorize}}\end{array}#
#\begin{array}{rcl}{324}{b}^2-49&=&(18b)^2-7^2\\&&\phantom{xxx}\blue{\text{recognize the square}}\\&=&(18b+7)(18b-7)\\&&\phantom{xxx}\blue{\text{factorize}}\end{array}#
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