What is expand 3x^4(4-x)^3 ?

The solution to expand 3x^4(4-x)^3 is 192x^4-144x^5+36x^6-3x^7

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expand 3x^4(4-x)^3

expand

3 x^{4} (4 - x)^{3}

192 x^{4} - 144 x^{5} + 36 x^{6} - 3 x^{7}

Solution steps

3 x^{4} (4 - x)^{3}

Expand

(4 - x)^{3} : 64 - 48 x + 12 x^{2} - x^{3}

= 3 x^{4} (64 - 48 x + 12 x^{2} - x^{3})

Distribute parentheses

= 3 x^{4} \cdot 64 + 3 x^{4} (- 48 x) + 3 x^{4} \cdot 12 x^{2} + 3 x^{4} (- x^{3})

Simplify

3 x^{4} \cdot 64 + 3 x^{4} (- 48 x) + 3 x^{4} \cdot 12 x^{2} + 3 x^{4} (- x^{3}) : 192 x^{4} - 144 x^{5} + 36 x^{6} - 3 x^{7}

= 192 x^{4} - 144 x^{5} + 36 x^{6} - 3 x^{7}

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What is expand 3x^4(4-x)^3 ?
The solution to expand 3x^4(4-x)^3 is 192x^4-144x^5+36x^6-3x^7