What is factor 12m^2*n+24m^3*n^2-36m^4*n^3+48m^5*n^4 ?

The solution to factor 12m^2*n+24m^3*n^2-36m^4*n^3+48m^5*n^4 is 12m^2n(1+2mn-3m^2n^2+4m^3n^3)

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factor 12m^2n+24m^3n^2-36m^4n^3+48m^5n^4

factor

12 m^{2} \cdot n + 24 m^{3} \cdot n^{2} - 36 m^{4} \cdot n^{3} + 48 m^{5} \cdot n^{4}

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

Solution steps

12 m^{2} n + 24 m^{3} n^{2} - 36 m^{4} n^{3} + 48 m^{5} n^{4}

Apply exponent rule:

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

m^{3} n^{2} = m^{2} mnn, m^{4} n^{3} = m^{2} m^{2} n n^{2}, m^{5} n^{4} = m^{2} m^{3} n n^{3}

= 12 m^{2} n + 24 m^{2} mnn - 36 m^{2} m^{2} n n^{2} + 48 m^{2} m^{3} n n^{3}

Rewrite

48

4 \cdot 12

Rewrite

- 36

3 \cdot 12

= 12 m^{2} n + 2 \cdot 12 m^{2} mnn + 3 \cdot 12 m^{2} m^{2} n n^{2} + 4 \cdot 12 m^{2} m^{3} n n^{3}

Factor out common term

12 m^{2} n

= 12 m^{2} n (1 + 2 mn - 3 m^{2} n^{2} + 4 m^{3} n^{3})

∣ i - j - 3 k ∣

(5 \cdot y^{2} - 10 \cdot z^{2})^{2}

(- 4 x^{4})^{2}

\frac{( 2 ^{x + 5} - 4 \cdot 2 ^{x} )}{( 16 \cdot 2 ^{x + 2} - 2 ^{x + 3} )}

(a - 1) \cdot (a + 1) \cdot (a^{2} + a + 1) \cdot (a^{2} - a + 1)

What is factor 12m^2*n+24m^3*n^2-36m^4*n^3+48m^5*n^4 ?
The solution to factor 12m^2*n+24m^3*n^2-36m^4*n^3+48m^5*n^4 is 12m^2n(1+2mn-3m^2n^2+4m^3n^3)