What is expand 6x^5(2x^2+9x-6)^2 ?

The solution to expand 6x^5(2x^2+9x-6)^2 is 24x^9+216x^8+342x^7-648x^6+216x^5

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expand 6x^5(2x^2+9x-6)^2

expand

6 x^{5} (2 x^{2} + 9 x - 6)^{2}

24 x^{9} + 216 x^{8} + 342 x^{7} - 648 x^{6} + 216 x^{5}

Solution steps

6 x^{5} (2 x^{2} + 9 x - 6)^{2}

(2 x^{2} + 9 x - 6)^{2} = 4 x^{4} + 36 x^{3} + 57 x^{2} - 108 x + 36

= 6 x^{5} (4 x^{4} + 36 x^{3} + 57 x^{2} - 108 x + 36)

Distribute parentheses

= 6 x^{5} \cdot 4 x^{4} + 6 x^{5} \cdot 36 x^{3} + 6 x^{5} \cdot 57 x^{2} + 6 x^{5} (- 108 x) + 6 x^{5} \cdot 36

Apply minus-plus rules

+ (- a) = - a

= 6 \cdot 4 x^{5} x^{4} + 6 \cdot 36 x^{5} x^{3} + 6 \cdot 57 x^{5} x^{2} - 6 \cdot 108 x^{5} x + 6 \cdot 36 x^{5}

Simplify

6 \cdot 4 x^{5} x^{4} + 6 \cdot 36 x^{5} x^{3} + 6 \cdot 57 x^{5} x^{2} - 6 \cdot 108 x^{5} x + 6 \cdot 36 x^{5} : 24 x^{9} + 216 x^{8} + 342 x^{7} - 648 x^{6} + 216 x^{5}

= 24 x^{9} + 216 x^{8} + 342 x^{7} - 648 x^{6} + 216 x^{5}

5 (e^{\frac{x}{10}} + e^{- \frac{x}{10}})

(e^{x} + e^{-} x)^{4}

\frac{1}{( 1 + x ) ( 1 - x )}

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

\frac{5}{s ^{2} ( s + 3 )}

What is expand 6x^5(2x^2+9x-6)^2 ?
The solution to expand 6x^5(2x^2+9x-6)^2 is 24x^9+216x^8+342x^7-648x^6+216x^5