Question Simplify the expression x6−6x4+12x2−8 Evaluate (x2−2)3Use (a−b)3=a3−3a2b+3ab2−b3 to expand the expression (x2)3−3(x2)2×2+3x2×22−23Solution x6−6x4+12x2−8 Show Solution Find the roots x1=−2,x2=2Alternative Form x1≈−1.414214,x2≈1.414214 Evaluate (x2−2)3To find the roots of the expression,set the expression equal to 0 (x2−2)3=0The only way a power can be 0 is when the base equals 0 x2−2=0Move the constant to the right-hand side and change its sign x2=0+2Removing 0 doesn't change the value,so remove it from the expression x2=2Take the root of both sides of the equation and remember to use both positive and negative roots x=±2Separate the equation into 2 possible cases x=2x=−2Solution x1=−2,x2=2Alternative Form x1≈−1.414214,x2≈1.414214 Show Solution
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