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Big Ideas Math Algebra 1 A Bridge to Success

BI

Big Ideas Math Algebra 1 A Bridge to Success View details

Maintaining Mathematical Proficiency

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Exercise 1 Page 477

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

(x+5)^2

We want to factor a perfect square trinomial. x^2+10x+25

How do we know that the expression is a perfect square trinomial? Well, let's ask a few questions.

Is the first term a perfect square?	x^2=( x)^2 ✓
Is the last term a perfect square?	25= 5^2 ✓
Is the middle term twice the product of 5 and x?	10x=2* 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 there is an addition sign in the middle. x^2+10x+25 ⇔ ( x+ 5)^2

Checking Our Answer

Check your answer ✓

Let's un-factor our answer and compare it with the given expression.

(x + 5)^2

ExpandPosPerfectSquare

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

x^2 + 10 x + 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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