How do you know if #x^2 + 10x + 25# is a perfect square?

3 Answers
Jul 10, 2018

Answer:

#(x+5)^2#

Explanation:

Using that

#a^2+2ab+b^2=(a+b)^2#
we get

#x^2+10x+25=(x+5)^2#

Jul 21, 2018

Answer:

See below:

Explanation:

Perfect square quadratics are of the form

#a^2+2ab+b^2#

In our case, #a=x# and #b=sqrt25#, or #b=5#

We can plug these values into our expression to get

#x^2+2*x*5+5^2#

This simplifies to

#x^2+10x+25#

Solidifying the fact that this is a perfect square, since #5# and #5# sum up to #10# and have a product of #25#, we can factor this as

#(x+5)^2#

Hope this helps!

Answer:

Compare given polynomial with the perfect square:#a^2+2ab+b^2=(a+b)^2#

Explanation:

Given that

#x^2+10x+25#

#=x^2+2(5)x+(5)^2#

Above expression is in form of #a^2+2ab+b^2# which is a perfect square #(a+b)^2# hence the given expression or polynomial is a perfect square given as

#(x+5)^2#