What is expand ((1.5)(1+15t^2)^2)/t ?

The solution to expand ((1.5)(1+15t^2)^2)/t is (1.5)/t+45t+337.5t^3

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expand ((1.5)(1+15t^2)^2)/t

expand

\frac{( 1.5 ) ( 1 + 15 t ^{2} ) ^{2}}{t}

\frac{1.5}{t} + 45 t + 337.5 t^{3}

Solution steps

\frac{( 1.5 ) ( 1 + 15 t ^{2} ) ^{2}}{t}

Remove parentheses:

(a) = a

= \frac{1.5 ( 1 + 15 t ^{2} ) ^{2}}{t}

(1 + 15 t^{2})^{2} = 1 + 30 t^{2} + 225 t^{4}

= \frac{1.5 ( 225 t ^{4} + 30 t ^{2} + 1 )}{t}

Expand

1.5 (1 + 30 t^{2} + 225 t^{4}) : 1.5 + 45 t^{2} + 337.5 t^{4}

= \frac{1.5 + 45 t ^{2} + 337.5 t ^{4}}{t}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{1.5 + 45 t ^{2} + 337.5 t ^{4}}{t} = \frac{1.5}{t} + \frac{45 t ^{2}}{t} + \frac{337.5 t ^{4}}{t}

= \frac{1.5}{t} + \frac{45 t ^{2}}{t} + \frac{337.5 t ^{4}}{t}

Cancel

\frac{45 t ^{2}}{t} : 45 t

= \frac{1.5}{t} + 45 t + \frac{337.5 t ^{4}}{t}

Cancel

\frac{337.5 t ^{4}}{t} : 337.5 t^{3}

= \frac{1.5}{t} + 45 t + 337.5 t^{3}

sec (x) (1 - sin (x)) (sec (x) + tan (x))

cos^{4} (x) (1 - tan^{4} (x)) + 2 sin^{2} (x)

6 (1 + 6)

(1 + \frac{26}{x}) x^{2} - 36

\frac{x ^{5} - 2 x + 1}{( x + 1 ) ( x ^{2} + 1 )}

What is expand ((1.5)(1+15t^2)^2)/t ?
The solution to expand ((1.5)(1+15t^2)^2)/t is (1.5)/t+45t+337.5t^3