Is #9x^2 + 42x + 49# a perfect square trinomial and how do you factor it?

2 Answers
Mar 5, 2018

Answer:

See below

Explanation:

We know that #(a+b)^2=a^2+2ab+b^2#

In our case: #9x^2+42x+49=3^2·x^2+2·9·7·x+7^2=(3x+7)^2# This it's the same that

#(3x+7)(3x+7)# is the factorization

Mar 5, 2018

If #9x^2 + 42x + 49# is a perfect square, then it must fit the pattern:

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

To verify whether it fits the pattern, we set the first term of the pattern equal to the first term of the given trinomial:

#a^2=9x^2#

Then we set the last term of the pattern equal to the last term of the given trinomial:

#b^2=49#

Taking the square root of both we obtain:

#a = 3x# and #b =7#

We can use this information to check whether the middle term is true:

#2ab = 42x#

#2(3x)7 = 42x#

#42x = 42x#

The middle term is true, therefore, we conclude that the given trinomial is a perfect square.

We can use the left side of the pattern to factor the given trinomial:

#(3x+7)^2 = 9x^2 + 42x + 49#