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Popular >

factor (x^2-1)^2+(2x)^2

Solution

factor

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

Solution

(x^{2} + 1)^{2}

Solution steps

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

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

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

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

2^{2} = 4

= (x + 1)^{2} (x - 1)^{2} + 4 x^{2}

(x + 1)^{2} : x^{2} + 2 x + 1

= (x^{2} + 2 x + 1) (x - 1)^{2} + 4 x^{2}

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

= (x^{2} + 2 x + 1) (x^{2} - 2 x + 1) + 4 x^{2}

Expand

(x^{2} + 2 x + 1) (x^{2} - 2 x + 1) : x^{4} - 2 x^{2} + 1

= x^{4} - 2 x^{2} + 1 + 4 x^{2}

Simplify

x^{4} - 2 x^{2} + 1 + 4 x^{2} : x^{4} + 2 x^{2} + 1

= x^{4} + 2 x^{2} + 1

Let

u = x^{2}

= u^{2} + 2 u + 1

Factor

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

= (u + 1) (u + 1)

Substitute back

u = x^{2}

= (x^{2} + 1) (x^{2} + 1)

Refine

= (x^{2} + 1)^{2}

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Frequently Asked Questions (FAQ)

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