Question
Factor the expression
(x2−2x+2)(x2+2x+2)
Evaluate
x4+4
Calculate
x4+2x3+2x2−2x3−4x2−4x+2x2+4x+4
Rewrite the expression
x2×x2+x2×2x+x2×2−2x×x2−2x×2x−2x×2+2x2+2×2x+2×2
Factor out x2 from the expression
x2(x2+2x+2)−2x×x2−2x×2x−2x×2+2x2+2×2x+2×2
Factor out −2x from the expression
x2(x2+2x+2)−2x(x2+2x+2)+2x2+2×2x+2×2
Factor out 2 from the expression
x2(x2+2x+2)−2x(x2+2x+2)+2(x2+2x+2)
Solution
(x2−2x+2)(x2+2x+2)
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Find the roots
x1=−1−i,x2=1+i
Evaluate
x4+4
To find the roots of the expression,set the expression equal to 0
x4+4=0
Move the constant to the right-hand side and change its sign
x4=0−4
Removing 0 doesn't change the value,so remove it from the expression
x4=−4
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4−4
Simplify the expression
More Steps

Evaluate
4−4
Rewrite the expression
2×(22+22i)
Apply the distributive property
2×22+2×22i
Multiply the numbers
More Steps

Evaluate
2×22
Multiply the numbers
22×2
Multiply the numbers
22
Reduce the fraction
1
1+2×22i
Multiply the numbers
1+i
x=±(1+i)
Separate the equation into 2 possible cases
x=1+ix=−1−i
Solution
x1=−1−i,x2=1+i
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