Could I please just have a brief explanation?

Why are you not able to factor the polynomial: 7m + 6mn + 3m^2 + 14n by grouping?

Could I please just have a brief explanation?

Why are you not able to factor the polynomial: 7m + 6mn + 3m^2 + 14n by grouping?

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This is factorable by grouping. One thing to consider is that terms are commutative, meaning they can be rearranged.

7m + 6mn + 3m^{2} + 14n

Rearrange terms and group 1st two and 2nd two==> (7m + 14n) + (6mn + 3m^{2})

From each group, factor out the GCF ==> 7**(m + 2n)** + 3m**(2n + m)**

Notice that the quantities in bold are identical (this let's you know you did the technique correctly). So now, the GCF of this new expression is the quantity (2n + m), so let's factor that out.

**(2n + m)**(7 + 3m) ==> note that if you distribute the bold quantity, you'd get the above expression again.

It looks like you can:

3m^{2} + 6mn + 7m + 14n

3m(m + 2n) + 7(m + 2n)

(3m + 7)(m + 2n)

3m^2 +3mn + 7m +14m:

Just look at the common factor between terms

3 m^2 + 3mn + 7m +14n

greatest common factor between 1st and 2nd/ also between 3rd & 4th is 3m, therefore

3m(m +n) +7 ( m+n)

now (m+n) is GCF between 2 terms:

(m+n)(3m+7)

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