Solve (5x^3-10x^2)(6x-50)^3

$$( 5 x ^ { 3 } - 10 x ^ { 2 } ) ( 6 x - 50 ) ^ { 3 }$$

Evaluate

$$40\left(x-2\right)x^{2}\left(3x-25\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(6x-50\right)^{3}.

$$\left(5x^{3}-10x^{2}\right)\left(216x^{3}-5400x^{2}+45000x-125000\right)$$

Use the distributive property to multiply 5x^{3}-10x^{2} by 216x^{3}-5400x^{2}+45000x-125000 and combine like terms.

$$1080x^{6}-29160x^{5}+279000x^{4}-1075000x^{3}+1250000x^{2}$$

Expand

$$1080x^{6}-29160x^{5}+279000x^{4}-1075000x^{3}+1250000x^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(6x-50\right)^{3}.

$$\left(5x^{3}-10x^{2}\right)\left(216x^{3}-5400x^{2}+45000x-125000\right)$$

Use the distributive property to multiply 5x^{3}-10x^{2} by 216x^{3}-5400x^{2}+45000x-125000 and combine like terms.

$$1080x^{6}-29160x^{5}+279000x^{4}-1075000x^{3}+1250000x^{2}$$