How to use special products to evalute 95 square?

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Answer 1 · 2018-02-24T12:50:37

#9025#

We have to evaluate #95^2#

#95# can be written as #(100-5)#. By extension, we can write #95^2# as #(100-5)^2#.

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

#100^2-2(100)(5)+5^2#

#10000-1000+25#

#9025# is equal to #95^2#

You can confirm that on any four-function calculator.

Answer 2 · 2018-02-24T12:55:14

9025 is the answer using binomial expansion

95=100-5

#95^2=(100-5)^2#

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

IN our case, for a=100, b=5;

#(100-5)^2=100^2-2xx100xx5+5^2#

#100^2=10000#

#2xx100xx5=1000#

#5^2=25#

Now,

#(100-5)^2=10000-1000+25#

#10000-1000=9000#

#9000+25=9025#

#(100-5)^2=9025#

#95^2=9025#