When simplified 1+ (x^4-12x^2 )^2 equals:

4x^44x^4+(x^4-1)^24x^4x^8-2x^4+1+4x^44x^4 (x^4+1)^2(2x^2)^2 x^4+12x^2x^22+12x^2, x^22+12x^2

smc

algebra intermediate

Problem

When simplified

1 + (\frac{x ^{4} - 1}{2 x ^{2}})^{2}

equals:

(A)

\frac{x ^{4} + 2 x ^{2} - 1}{2 x ^{2}}

(B)

\frac{x ^{4} - 1}{2 x ^{2}}

(C)

\frac{x ^{2} + 1}{2}

(D)

\frac{x ^{2}}{2}

(E)

\frac{x ^{2}}{2} + \frac{1}{2 x ^{2}}

Solution

\frac{4 x ^{4}}{4 x ^{4}} + \frac{( x ^{4} - 1 ) ^{2}}{4 x ^{4}} ⟹ \frac{x ^{8} - 2 x ^{4} + 1 + 4 x ^{4}}{4 x ^{4}} ⟹ \frac{( x ^{4} + 1 ) ^{2}}{( 2 x ^{2} ) ^{2}} ⟹ \frac{x ^{4} + 1}{2 x ^{2}} ⟹ \frac{x ^{2}}{2} + \frac{1}{2 x ^{2}}

\frac{x ^{2}}{2} + \frac{1}{2 x ^{2}}

Final answer