Clare claims that [math](10+3)(10-3)[/math] is equivalent to [math]10^2-3^2[/math] and [math](20+1)(20-1)[/math] is equivalent to [math]20^2-1^2[/math]. Do you agree? Show your reasoning.
Use your observations from the first question and evaluate [math]\left(100+5\right)\left(100-5\right)[/math]. Show your reasoning.[br]
Check your answer by computing [math]105\cdot95[/math].[br]
Is [math]\left(x+4\right)\left(x-4\right)[/math] equivalent to [math]x^2-4^2[/math]? Support your answer without a diagram.
Explain how your work in the previous questions can help you mentally evaluate [math]22\cdot18[/math] and [math]45\cdot35[/math].[br]
[size=150][size=100]Here is a shortcut that can be used to mentally square any two-digit number. Let’s take [math]83^2[/math], for example.[br][list][*]83 is [math]80+3[/math].[/*][*]Compute [math]80^2[/math] and [math]3^2[/math], which give 6,400 and 9. Add these values to get 6,409.[/*][*]Compute [math]80\cdot3[/math], which is 240. Double it to get 480.[/*][*]Add 6,409 and 480 to get 6,889.[/*][/list][/size][br][/size]Try using this method to find the squares of some other two-digit numbers. (With some practice, it is possible to get really fast at this!) Then, explain why this method works.[br]