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Popolare Algebra >

espandere ((6-25x^2)^2)/(900)

Soluzione

espandere

\frac{( 6 - 25 x ^{2} ) ^{2}}{900}

Soluzione

\frac{25 x ^{4}}{36} - \frac{x ^{2}}{3} + \frac{1}{25}

Fasi della soluzione

\frac{( 6 - 25 x ^{2} ) ^{2}}{900}

(6 - 25 x^{2})^{2} = 36 - 300 x^{2} + 625 x^{4}

= \frac{36 - 300 x ^{2} + 625 x ^{4}}{900}

Applica la regola delle frazioni:

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

\frac{36 - 300 x ^{2} + 625 x ^{4}}{900} = \frac{36}{900} - \frac{300 x ^{2}}{900} + \frac{625 x ^{4}}{900}

= \frac{36}{900} - \frac{300 x ^{2}}{900} + \frac{625 x ^{4}}{900}

Cancellare

\frac{36}{900} : \frac{1}{25}

= \frac{1}{25} - \frac{300 x ^{2}}{900} + \frac{625 x ^{4}}{900}

Cancellare

\frac{300 x ^{2}}{900} : \frac{x ^{2}}{3}

= \frac{1}{25} - \frac{x ^{2}}{3} + \frac{625 x ^{4}}{900}

Cancellare

\frac{625 x ^{4}}{900} : \frac{25 x ^{4}}{36}

= \frac{1}{25} - \frac{x ^{2}}{3} + \frac{25 x ^{4}}{36}

Riscrivere in forma standard

= \frac{25 x ^{4}}{36} - \frac{x ^{2}}{3} + \frac{1}{25}

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