What is factor m^4+m^2n^2+n^4 ?

The solution to factor m^4+m^2n^2+n^4 is (m^2+n^2+mn)(m^2+n^2-mn)

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factor m^4+m^2n^2+n^4

factor

m^{4} + m^{2} n^{2} + n^{4}

(m^{2} + n^{2} + mn) (m^{2} + n^{2} - mn)

Solution steps

m^{4} + m^{2} n^{2} + n^{4}

Add and subtract

m^{2} n^{2}

= m^{4} + 2 m^{2} n^{2} + n^{4} - m^{2} n^{2}

Factor

m^{4} + 2 m^{2} n^{2} + n^{4} : (m^{2} + n^{2})^{2}

= (m^{2} + n^{2})^{2} - m^{2} n^{2}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

m^{2} n^{2} = (mn)^{2}

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

Factor

(m^{2} + n^{2})^{2} - (mn)^{2} : (m^{2} + n^{2} + mn) (m^{2} + n^{2} - mn)

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

lo g_{5} (100) - lo g_{5} (4)

(3 x - 4 y)^{3}

(y^{2} - 3 y) (y^{2} + 3 y)

(m + n) (m - n)

- 8^{\frac{2}{3}}

What is factor m^4+m^2n^2+n^4 ?
The solution to factor m^4+m^2n^2+n^4 is (m^2+n^2+mn)(m^2+n^2-mn)