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McGraw Hill Integrated II, 2012 View details

9. Perfect Squares

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Exercise 13 Page 68

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

Perfect Square?: Yes.
Factored Form: (4x-7)^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?	16x^2= (4x)^2 ✓
Is the last term a perfect square?	49= 7^2 ✓
Is the middle term twice the product of 7 and 4x?	56x=2* 7* 4x ✓

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 that there is a subtraction sign in the middle. 16x^2-56a+49 ⇔ ( 4x- 7)^2

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

(4x - 7 )^2

ExpandNegPerfectSquare

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

16x^2 - 56x + 49

After expanding, 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 13 Page 68

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