How do you know if #100a^2 + 100a + 25# is a perfect square trinomial and how do you factor it?

1 Answer
May 19, 2018

Answer:

#(10a+5)^2#

Explanation:

For a prefect square trinomial. look for the following properties,

First and third terms must be perfect squares.

#sqrt(100a^2) = 10a" "and sqrt25 = 5#

Check whether the middle term is the product of the two square roots, doubled.

#10a xx 5 = 50a" "rarr 2 xx 50a = 100a#

If these properties are present the trinomial is a perfect square.

To factorise:

#100a^2 +100a +25#

The binomial is made up of:

  • square root of the first term #(10a)#
  • the sign of the second term #(+)#
  • the square root of the third term #5#

#=(10a+5)^2#