Solve (49-3x)^{3}*7,45x(-175,3)^0*(2^3*5^3)^-1

$$( 49 - 3 x ) ^ { 3 } \times 7,45 x ( - 175,3 ) ^ { 0 } \times ( 2 ^ { 3 } \times 5 ^ { 3 } ) ^ { - 1 }$$

Evaluate

$$\frac{149x\left(49-3x\right)^{3}}{20000}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(49-3x\right)^{3}.

$$\left(117649-21609x+1323x^{2}-27x^{3}\right)\times 7,45x\left(-175,3\right)^{0}\times \left(2^{3}\times 5^{3}\right)^{-1}$$

Calculate -175,3 to the power of 0 and get 1.

$$\left(117649-21609x+1323x^{2}-27x^{3}\right)\times 7,45x\times 1\times \left(2^{3}\times 5^{3}\right)^{-1}$$

Multiply 7,45 and 1 to get 7,45.

$$\left(117649-21609x+1323x^{2}-27x^{3}\right)\times 7,45x\times \left(2^{3}\times 5^{3}\right)^{-1}$$

Calculate 2 to the power of 3 and get 8.

$$\left(117649-21609x+1323x^{2}-27x^{3}\right)\times 7,45x\times \left(8\times 5^{3}\right)^{-1}$$

Calculate 5 to the power of 3 and get 125.

$$\left(117649-21609x+1323x^{2}-27x^{3}\right)\times 7,45x\times \left(8\times 125\right)^{-1}$$

Multiply 8 and 125 to get 1000.

$$\left(117649-21609x+1323x^{2}-27x^{3}\right)\times 7,45x\times 1000^{-1}$$

Calculate 1000 to the power of -1 and get \frac{1}{1000}.

$$\left(117649-21609x+1323x^{2}-27x^{3}\right)\times 7,45x\times \frac{1}{1000}$$

Multiply 7,45 and \frac{1}{1000} to get \frac{149}{20000}.

$$\left(117649-21609x+1323x^{2}-27x^{3}\right)\times \frac{149}{20000}x$$

Use the distributive property to multiply 117649-21609x+1323x^{2}-27x^{3} by \frac{149}{20000}.

$$\left(\frac{17529701}{20000}-\frac{3219741}{20000}x+\frac{197127}{20000}x^{2}-\frac{4023}{20000}x^{3}\right)x$$

Use the distributive property to multiply \frac{17529701}{20000}-\frac{3219741}{20000}x+\frac{197127}{20000}x^{2}-\frac{4023}{20000}x^{3} by x.

$$\frac{17529701}{20000}x-\frac{3219741}{20000}x^{2}+\frac{197127}{20000}x^{3}-\frac{4023}{20000}x^{4}$$

Differentiate w.r.t. x

$$-\frac{149\left(12x-49\right)\left(3x-49\right)^{2}}{20000}$$