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Popular >

factor a^4-18a^2+81

Solution

factor

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

Solution

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

Solution steps

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

Let

u = a^{2}

= u^{2} - 18 u + 81

Factor

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

= (u - 9)^{2}

Substitute back

u = a^{2}

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

Factor

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

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

Apply exponent rule:

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

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

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

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Frequently Asked Questions (FAQ)

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