What is (1/(y^2)-3/(y^4))(y+5y^3) ?

The solution to (1/(y^2)-3/(y^4))(y+5y^3) is ((y^2-3)(1+5y^2))/(y^3)

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simplify (1/(y^2)-3/(y^4))(y+5y^3)

simplify

(\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) (y + 5 y^{3})

\frac{( y ^{2} - 3 ) ( 1 + 5 y ^{2} )}{y ^{3}}

Solution steps

(\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) (y + 5 y^{3})

Join

\frac{1}{y ^{2}} - \frac{3}{y ^{4}} : \frac{y ^{2} - 3}{y ^{4}}

= \frac{y ^{2} - 3}{y ^{4}} (y + 5 y^{3})

Apply the fraction rule:

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

= \frac{( y ^{2} - 3 ) ( y + 5 y ^{3} )}{y ^{4}}

Factor

y + 5 y^{3} : y (1 + 5 y^{2})

= \frac{( y ^{2} - 3 ) y ( 1 + 5 y ^{2} )}{y ^{4}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

y^{4} = y y^{3}

= \frac{( y ^{2} - 3 ) y ( 1 + 5 y ^{2} )}{y y ^{3}}

Cancel the common factor:

y

= \frac{( y ^{2} - 3 ) ( 1 + 5 y ^{2} )}{y ^{3}}

(2 x^{2} + x - 3)^{8}

\frac{πk ( b ^{2} + z ^{2} - 2 b z )}{2 a}

(x^{\frac{6}{5}} + 2 x) e^{x}

(x - 2 - 2) (x - 2 + 2)

\frac{2 ( s ^{2} - 3 )}{( s + 2 ) ^{2} ( s - 2 ) ^{2}}

What is (1/(y^2)-3/(y^4))(y+5y^3) ?
The solution to (1/(y^2)-3/(y^4))(y+5y^3) is ((y^2-3)(1+5y^2))/(y^3)