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Popular >

factor y^4-2y^2+1

Solution

factor

y^{4} - 2 y^{2} + 1

Solution

(y + 1)^{2} (y - 1)^{2}

Solution steps

y^{4} - 2 y^{2} + 1

Let

u = y^{2}

= u^{2} - 2 u + 1

Factor

u^{2} - 2 u + 1 : (u - 1)^{2}

= (u - 1)^{2}

Substitute back

u = y^{2}

= (y^{2} - 1)^{2}

Factor

y^{2} - 1 : (y + 1) (y - 1)

= ((y + 1) (y - 1))^{2}

Apply exponent rule:

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

((y + 1) (y - 1))^{2} = (y + 1)^{2} (y - 1)^{2}

= (y + 1)^{2} (y - 1)^{2}

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Frequently Asked Questions (FAQ)

What is factor y^4-2y^2+1 ?
The solution to factor y^4-2y^2+1 is (y+1)^2(y-1)^2