A square has a side length of 4a. One dimension is decreased by 5 and the other dimension is decreased by 5. Expand and simplify the expression that represents the area of the resulting rectangle
Mathematics · High School · Thu Feb 04 2021
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given that :- A square has a side length = 4a so its breath is also = 4a because square have same size of length and breath.
now, One dimension is decreased by 5 and the other dimension is decreased by 5 means length of square is decreased by 5 and breath also decreased by 5
now, resulting square have length=4a-5 and breath=4a-5
so, area of resulting rectangle is = length* breath
=(4a-5)(4a-5)
here, using formula (a-b)(a-b)=(a-b)^2
=a^2+b^2-2ab
here, a=4a and b=5
put values in formula:- a^2+b^2-2ab
=(4a)^2+5^2-2.4a.5
=16a^2+25-40a (simplified expression of resulting rectangle)