body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Dashboard

McGraw Hill Integrated II, 2012 View details

9. Perfect Squares

Finish the assignment

Continue to next subchapter

Exercise 19 Page 69

Is there a greatest common factor between all of the terms in the given expression? If so, factor that out first.

8(y+5z)(y-5z)

Practice makes perfect

We want to completely factor the given expression. To do so, we will first identify and factor out the greatest common factor (GCF), a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent. The GCF of the given expression is 8.

8y^2-200z^2

SplitIntoFactors

Split into factors

8(y^2)- 8(25z^2)

FactorOut

Factor out 8

8(y^2-25z^2)

Notice that this is a difference of squares. Let's rewrite our expression as a binomial multiplied by it's conjugate. 8(y^2-25z^2) ⇔ 8(y+5z)(y-5z)

Checking Our Answer

Check Our Answer ✓

We can expand our answer and compare it with the given expression.

8 (y +5z) (y - 5z)

Distr

Distribute 8

(8y +40z) (y - 5z)

Distr

Distribute 8y+40z

y (8y +40z) - (5z)(8y +40z)

Distr

Distribute y

8 y^2 + 40zy - (5z)(8y +40z)

Distr

Distribute -5z

8y^2+40zy-40zy-200z^2

SubTerm

Subtract term

8y^2-200z^2

We can see above that after expanding and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!

Subchapter links

Exercises p.68-71

Exercise 19 Page 69

Hints

Check the answer

Practice exercises

Asses your skill

Checking Our Answer