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McGraw Hill Glencoe Algebra 1 Texas, 2016

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McGraw Hill Glencoe Algebra 1 Texas, 2016 View details

9. Perfect Squares

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Exercise 1 Page 526

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

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

Practice makes perfect

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

Is the first term a perfect square?	$25 x^{2} = 5^{2} x^{2} = (5 x)^{2}$ $✓$
Is the last term a perfect square?	$36 = 6^{2}$ $✓$
Is the middle term $t w i c e$ the product of $6$ and $5 x$ ?	$60 x = 2 \cdot 6 \cdot 5 x$ $✓$

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.

25 x^{2} + 60 x + 36 \Leftrightarrow (5 x + 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

$(a + b)^{2} = a^{2} + 2 a b + b^{2}$

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!

Subchapter links

Check Your Understanding p.526

Practice and Problem Solving p.526-528

H.O.T. Problems p.528

Preparing for Assessment p.529