Exercise 1 Page 526

To determine if an expression is a perfect square trinomial, we need to ask ourselves three questions.

Is the first term a perfect square?	25x^2= 5^2x^2=( 5x)^2 ✓
Is the last term a perfect square?	36= 6^2 ✓
Is the middle term twice the product of 6 and 5x?	60x= 2* 6* 5x ✓

As we can see, the answer to all three questions is yes! Therefore, we can write the trinomial as the square of a binomial. Note that there is an addition sign in the middle. 25x^2+60x+36 ⇔ ( 5x+ 6)^2

Checking Our Answer

Checking Our Answer ✓

Let's expand our answer and compare it with the given expression.

(5 x + 6)^2

ExpandPosPerfectSquare

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

25 x^2 + 60 x + 36

After expanding and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!