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McGraw Hill Integrated II, 2012 View details

9. Perfect Squares

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Exercise 1 Page 68

To factor a perfect square trinomial, the first and last terms have to be perfect squares.

Perfect Square?: Yes
Factor: (5x+6)^2

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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

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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!

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Exercises p.68-71

Exercise 1 Page 68

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