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Pearson Algebra 1 Common Core, 2015

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Pearson Algebra 1 Common Core, 2015 View details

7. Factoring Special Cases

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Exercise 1 Page 526

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

(y - 8 )^2

Practice makes perfect

We want to factor a perfect square trinomial. y^2-16y+64

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?	y^2= y^2 ✓
Is the last term a perfect square?	64= 8^2 ✓
Is the middle term twice the product of 8 and y?	16y=2* 8* y ✓

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.

y^2- 16y+ 64

SplitIntoFactors

Split into factors

y^2-2y(8)+64

Write as a power

y^2- 2 y( 8)+ 8^2

FacNegPerfectSquare

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

( y- 8)^2

Checking Our Answer

Check your answer ✓

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

(y - 8 )^2

ExpandNegPerfectSquare

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

y^2-2y(8)+8^2

Multiply

y^2-16y+8^2

Calculate power

y^2 - 16y + 64 ✓

After expanding and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!

Subchapter links

Lesson Check p.526

Practice and Problem-Solving Exercises p.526-528

Standardized Test Prep p.528

Mixed Review p.528