I know how to factor a trinomial into a product of two binomials. I know how to do the foil method. But how do I factor an equation like this!?

(m-5)(m+4)+8

I need to know what something like this simplifies to and how to do it. Please help me!

OfficialBubbleTanks
Oct 26, 2017

#1**+3 **

First expand the bracketed terms to get:

(m-5)(m+4) + 8 → m^{2} - m - 20 + 8 → m^{2} - m - 12

Now notice that 12 is the product of 4 and 3, and 1 is the difference between 4 and 3.

Taking the signs into account this gives us: m^{2} - m - 12 = (m - 4)(m + 3)

Alan
Oct 26, 2017

#3**+1 **

**I know how to factor a trinomial into a product of two binomials. **

**I know how to do the foil method.**

**But how do I factor an equation like this!?**

**(m-5)(m+4)+8**

\(\begin{array}{|rcll|} \hline && \mathbf{(m-5)(m+4)+8} \\ &=& (m-5)(m+4)+4+4 \\ &=& (m-5)(m+4)+4+4 +m-m\\ &=& (m-5)(m+4)+(m+4)-(m-4) \\ &=& (m+4)[(m-5)+1]-(m-4) \\ &=& (m+4)(m-4)-(m-4) \\ &=& (m-4)[(m+4)-1] \\ &\mathbf{=}& \mathbf{(m-4)(m+3)} \\ \hline \end{array}\)

heureka
Oct 27, 2017