Multiply (sic) #(2x-5)^2# ?

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Answer 1 · 2017-08-24T03:24:07

#4x^2-20x+25#

#(2x-5)^2#

[N.B. By "multiply" I assume you mean expand]

Remember: #(a-b)^2 = a^2-2ab+b^2#

We can prove this by expanding term by term as follows:

#(a-b)^2 = (a-b)(a-b)#

#= a(a-b) - b(a-b)#

#=a^2-ab -ba +b^2#

Since #ba = ab#

#=a^2-ab -ab +b^2#

#= a^2-2ab+b^2#

In our example #a=2x and b=5#

#:. (2x-5)^2 =(2x)^2 - 2xx 2x xx 5 +5^2#

#= 4x^2 -20x +25#