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Popular >

factor m^4-18m^2+81

Solution

factor

m^{4} - 18 m^{2} + 81

Solution

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

Solution steps

m^{4} - 18 m^{2} + 81

Let

u = m^{2}

= u^{2} - 18 u + 81

Factor

u^{2} - 18 u + 81 : (u - 9)^{2}

= (u - 9)^{2}

Substitute back

u = m^{2}

= (m^{2} - 9)^{2}

Factor

m^{2} - 9 : (m + 3) (m - 3)

= ((m + 3) (m - 3))^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

((m + 3) (m - 3))^{2} = (m + 3)^{2} (m - 3)^{2}

= (m + 3)^{2} (m - 3)^{2}

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Frequently Asked Questions (FAQ)

What is factor m^4-18m^2+81 ?
The solution to factor m^4-18m^2+81 is (m+3)^2(m-3)^2