展开 (tan(x)-4)(tan(x)+4)(tan(x)-2)(tan(x)+2)

解答

展开

(tan (x) - 4) (tan (x) + 4) (tan (x) - 2) (tan (x) + 2)

tan^{4} (x) - 20 tan^{2} (x) + 64

求解步骤

(tan (x) - 4) (tan (x) + 4) (tan (x) - 2) (tan (x) + 2)

展开

(tan (x) - 4) (tan (x) + 4) (tan (x) - 2) (tan (x) + 2) : (tan^{2} (x) - 16) (tan (x) - 2) (tan (x) + 2)

= (tan^{2} (x) - 16) (tan (x) - 2) (tan (x) + 2)

Apply Difference of Two Squares

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

= (tan^{2} (x) - 16) (tan^{2} (x) - 4)

Apply FOIL method

(tan^{2} (x) - 16) (tan^{2} (x) - 4) : tan^{4} (x) - 20 tan^{2} (x) + 64

= tan^{4} (x) - 20 tan^{2} (x) + 64

s im pl i f y 5 x (x - 8 x)

e x p an d \frac{2 ( - x ^{2} + 7 )}{( x ^{2} + 7 ) ^{2}}

e x p an d (1 + ln (2))^{3}

e x p an d x^{2} (cos^{2} (y) - sin^{2} (y))

s im pl i f y (2 x + 4) (x)