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McGraw Hill Integrated II, 2012 View details

9. Perfect Squares

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Exercise 14 Page 68

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

Perfect Square?: Yes Factored Form: (9x-5)^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?	81x^2=( 9x)^2 ✓
Is the last term a perfect square?	25= 5^2 ✓
Is the middle term twice the product of 5 and 9x?	90x= 2* 5* 9x ✓

As we can see, the answer to the three questions above is yes! Therefore, we can write the trinomial as the square of a binomial. Note there is a subtraction sign in the middle. 81x^2-90x+25 ⇔ ( 9x- 5)^2

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

(9x - 5 )^2

ExpandNegPerfectSquare

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

81x^2 - 90x + 25

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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Exercise 14 Page 68

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