Exercise 19 Page 69

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!