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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
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3+0 Answers

 #1
avatar+26328 
+3

First expand the bracketed terms to get:

 

(m-5)(m+4) + 8 → m2 - m - 20 + 8 → m2 - 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: m2 - m - 12 = (m - 4)(m + 3)

Alan  Oct 26, 2017
 #2
avatar+237 
+3

Thank you so much! This is very helpful information!

coolcoolcoolcoolcoolcoolcoolcoolcool

OfficialBubbleTanks  Oct 26, 2017
 #3
avatar+18712 
+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

 

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

 

laugh

heureka  Oct 27, 2017

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