Calculating with letters: Special products
The difference of two squares
The difference of two squares can be factored into two terms via the following formula. \[a^2-b^2=(a+b)(a-b)\] You get the left-hand side by applying the banana formula on the right-hand side and by cancelling terms against each other.
This formula can be again read and applied like the previous special formulas from left to right or vice versa. For this, you must recognise a square.
\({16}{b}^2-289=(4b+17)(4b-17)\) because \({16}{b}^2=(4b)^2\) and \(289=17^2\) so that the formula for the difference of two squares can be applied.
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