What is expand (5x-x^3)^2sqrt(8+x^2) ?

The solution to expand (5x-x^3)^2sqrt(8+x^2) is 25x^2sqrt(8+x^2)-10x^4sqrt(8+x^2)+x^6sqrt(8+x^2)

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expand (5x-x^3)^2sqrt(8+x^2)

expand

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

25 x^{2} 8 + x^{2} - 10 x^{4} 8 + x^{2} + x^{6} 8 + x^{2}

Solution steps

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

Expand

(5 x - x^{3})^{2} : 25 x^{2} - 10 x^{4} + x^{6}

= (25 x^{2} - 10 x^{4} + x^{6}) 8 + x^{2}

= 8 + x^{2} (25 x^{2} - 10 x^{4} + x^{6})

Apply the distributive law:

m (a + b + c) = ma + mb + m c

8 + x^{2} (25 x^{2} - 10 x^{4} + x^{6}) = 8 + x^{2} \cdot 25 x^{2} + 8 + x^{2} (- 10 x^{4}) + 8 + x^{2} x^{6}

= 8 + x^{2} \cdot 25 x^{2} + 8 + x^{2} (- 10 x^{4}) + 8 + x^{2} x^{6}

Simplify

8 + x^{2} \cdot 25 x^{2} + 8 + x^{2} (- 10 x^{4}) + 8 + x^{2} x^{6} : 25 x^{2} 8 + x^{2} - 10 x^{4} 8 + x^{2} + x^{6} 8 + x^{2}

= 25 x^{2} 8 + x^{2} - 10 x^{4} 8 + x^{2} + x^{6} 8 + x^{2}

\frac{x ^{2}}{( x + 1 ) ^{3}}

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

6 a^{\frac{7}{4}} \cdot (a^{\frac{7}{4}} + a^{\frac{3}{4}})

(3 + 5)^{2}

(2 x - 5 i)^{2}

What is expand (5x-x^3)^2sqrt(8+x^2) ?
The solution to expand (5x-x^3)^2sqrt(8+x^2) is 25x^2sqrt(8+x^2)-10x^4sqrt(8+x^2)+x^6sqrt(8+x^2)