Factoring by Grouping =!

How do we factor by grouping? 

In order to factor by grouping, basic simplifying and factoring is needed.

Simplifying: clearing parentheses, combining like terms by adding coefficients then combining constants. 

For example.

3(x+2) + 5(x+2)

First distribute to clear parentheses.

3x + 6 + 5x + 10

Next combine like terms by adding coefficients.

8x + 16

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Now do some Factoring.

x² - 5x -36

(x - 9)(x + 4)



 Back to Simplifying: Now try grouping instead of combining like terms.

3(x + 2) + 5(x +2)

Now ask: What does this equation have in common with itself?

The answer is : (x+2)

So place 3 and 5 in parentheses as well.   

(3+5)(x+2) *Don`t foil.

Then you`ll get 8(x+2)     
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Now for a problem involving Factoring by Grouping.

x³ + 3x² - 4x - 12

• Separate the equation 

x³+ 3x² |  -4x -12

• Simplify each side

x² (x + 3) |  -4 (x +3)   

• Trick is to have the (x + 3) on both sides. Ask: What do they have in common?
• Then group.

(x²-4)(x+3)

• Factor (x²-4) to get the perfect answer.

(x+2)(x-2)(x+3)