factor the polynomial....

Question

m^2-4m+4-n^2+6n-9

Answer 1

Hi Kelly,

m² -4m +4 -n² +6n -9

Grouping gives (m² -4m +4) - (n² -6n +9)

Factoring gives (m -2)² - (n-3)²

Using the difference of two squares above gives,

[(m-2)+(n-3)] [(m-2) - (n-3)]

Simplifying each factor gives (m+n-5)(m-n+1)

Factoring can be fun!

Answer 2

m² - 4m + 4 - n² + 6n - 9

 

(m² - 4m + 4) - (n² - 6n + 9)

 

You can factor each of these quadratics separately:

 

(m-2)² - (n-3)²

 

Now the above expression is a "difference of squares", x² - a² = (x-a)(x+a), so:

 

(m-2)² - (n-3)² = ((m-2)-(n-3))*((m-2)+(n-3)) = (m-n+1)(m+n-5)