What is factor 12m^5n^2-6m^2n^3+3mn ?

The solution to factor 12m^5n^2-6m^2n^3+3mn is 3mn(4m^4n-2mn^2+1)

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factor 12m^5n^2-6m^2n^3+3mn

factor

12 m^{5} n^{2} - 6 m^{2} n^{3} + 3 mn

3 mn (4 m^{4} n - 2 m n^{2} + 1)

Solution steps

12 m^{5} n^{2} - 6 m^{2} n^{3} + 3 mn

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

m^{5} n^{2} = m m^{4} nn, m^{2} n^{3} = mmn n^{2}

= 12 m m^{4} nn - 6 mmn n^{2} + 3 mn

Rewrite

- 6

2 \cdot 3

Rewrite

12

4 \cdot 3

= 4 \cdot 3 m m^{4} nn + 2 \cdot 3 mmn n^{2} + 3 mn

Factor out common term

3 mn

= 3 mn (4 m^{4} n - 2 m n^{2} + 1)

8 + 32

4 m^{4} - 25 n^{2}

\frac{25}{9} a^{4} - 36 b^{2}

\frac{36 a ^{5} b ^{3}}{3 a ^{2} b}

(x - 1) (x + 2)^{2} - (x - 1)^{2} (x + 2)

What is factor 12m^5n^2-6m^2n^3+3mn ?
The solution to factor 12m^5n^2-6m^2n^3+3mn is 3mn(4m^4n-2mn^2+1)