What is factor 21m^5n-7m^4n^2+7m^3n^3-7m^2n ?

The solution to factor 21m^5n-7m^4n^2+7m^3n^3-7m^2n is 7m^2n(3m^3-m^2n+mn^2-1)

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factor 21m^5n-7m^4n^2+7m^3n^3-7m^2n

factor

21 m^{5} n - 7 m^{4} n^{2} + 7 m^{3} n^{3} - 7 m^{2} n

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

Solution steps

21 m^{5} n - 7 m^{4} n^{2} + 7 m^{3} n^{3} - 7 m^{2} n

Apply exponent rule:

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

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

= 21 m^{2} m^{3} n - 7 m^{2} m^{2} nn + 7 m^{2} mn n^{2} - 7 m^{2} n

Rewrite

21

3 \cdot 7

= 3 \cdot 7 m^{2} m^{3} n - 7 m^{2} m^{2} nn + 7 m^{2} mn n^{2} - 7 m^{2} n

Factor out common term

7 m^{2} n

= 7 m^{2} n (3 m^{3} - m^{2} n + m n^{2} - 1)

2 - 7 y \leq 16 y - 13

∣ 4 x + 2 ∣ + 3 > 21

4 x^{3} + 4 x^{2} + x

5 x^{2} + 8 x - 4 = 0

x^{2} - 10 x + 5 = 0

What is factor 21m^5n-7m^4n^2+7m^3n^3-7m^2n ?
The solution to factor 21m^5n-7m^4n^2+7m^3n^3-7m^2n is 7m^2n(3m^3-m^2n+mn^2-1)