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Popular >

factor x^4-50x^2+625

Solution

factor

x^{4} - 50 x^{2} + 625

Solution

(x + 5)^{2} (x - 5)^{2}

Solution steps

x^{4} - 50 x^{2} + 625

Let

u = x^{2}

= u^{2} - 50 u + 625

Factor

u^{2} - 50 u + 625 : (u - 25)^{2}

= (u - 25)^{2}

Substitute back

u = x^{2}

= (x^{2} - 25)^{2}

Factor

x^{2} - 25 : (x + 5) (x - 5)

= ((x + 5) (x - 5))^{2}

Apply exponent rule:

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

((x + 5) (x - 5))^{2} = (x + 5)^{2} (x - 5)^{2}

= (x + 5)^{2} (x - 5)^{2}

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Frequently Asked Questions (FAQ)

What is factor x^4-50x^2+625 ?
The solution to factor x^4-50x^2+625 is (x+5)^2(x-5)^2