Solve 5(left(x-4right)^3-2(x-4)-8(4left(6-3xright)^2-6(6-3x)+8)

$$5( { \left(x-4 \right) }^{ 3 } -2(x-4)-8(4 { \left(6-3x \right) }^{ 2 } -6(6-3x)+8)$$

Evaluate

$$5\left(x^{3}-300x^{2}+1054x-984\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-4\right)^{3}.

$$5\left(x^{3}-12x^{2}+48x-64-2\left(x-4\right)-8\left(4\left(6-3x\right)^{2}-6\left(6-3x\right)+8\right)\right)$$

Use the distributive property to multiply -2 by x-4.

$$5\left(x^{3}-12x^{2}+48x-64-2x+8-8\left(4\left(6-3x\right)^{2}-6\left(6-3x\right)+8\right)\right)$$

Combine 48x and -2x to get 46x.

$$5\left(x^{3}-12x^{2}+46x-64+8-8\left(4\left(6-3x\right)^{2}-6\left(6-3x\right)+8\right)\right)$$

Add -64 and 8 to get -56.

$$5\left(x^{3}-12x^{2}+46x-56-8\left(4\left(6-3x\right)^{2}-6\left(6-3x\right)+8\right)\right)$$

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

$$5\left(x^{3}-12x^{2}+46x-56-8\left(4\left(36-36x+9x^{2}\right)-6\left(6-3x\right)+8\right)\right)$$

Use the distributive property to multiply 4 by 36-36x+9x^{2}.

$$5\left(x^{3}-12x^{2}+46x-56-8\left(144-144x+36x^{2}-6\left(6-3x\right)+8\right)\right)$$

Use the distributive property to multiply -6 by 6-3x.

$$5\left(x^{3}-12x^{2}+46x-56-8\left(144-144x+36x^{2}-36+18x+8\right)\right)$$

Subtract 36 from 144 to get 108.

$$5\left(x^{3}-12x^{2}+46x-56-8\left(108-144x+36x^{2}+18x+8\right)\right)$$

Combine -144x and 18x to get -126x.

$$5\left(x^{3}-12x^{2}+46x-56-8\left(108-126x+36x^{2}+8\right)\right)$$

Add 108 and 8 to get 116.

$$5\left(x^{3}-12x^{2}+46x-56-8\left(116-126x+36x^{2}\right)\right)$$

Use the distributive property to multiply -8 by 116-126x+36x^{2}.

$$5\left(x^{3}-12x^{2}+46x-56-928+1008x-288x^{2}\right)$$

Subtract 928 from -56 to get -984.

$$5\left(x^{3}-12x^{2}+46x-984+1008x-288x^{2}\right)$$

Combine 46x and 1008x to get 1054x.

$$5\left(x^{3}-12x^{2}+1054x-984-288x^{2}\right)$$

Combine -12x^{2} and -288x^{2} to get -300x^{2}.

$$5\left(x^{3}-300x^{2}+1054x-984\right)$$

Use the distributive property to multiply 5 by x^{3}-300x^{2}+1054x-984.

$$5x^{3}-1500x^{2}+5270x-4920$$

Expand

$$5x^{3}-1500x^{2}+5270x-4920$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-4\right)^{3}.

$$5\left(x^{3}-12x^{2}+48x-64-2\left(x-4\right)-8\left(4\left(6-3x\right)^{2}-6\left(6-3x\right)+8\right)\right)$$

Use the distributive property to multiply -2 by x-4.

$$5\left(x^{3}-12x^{2}+48x-64-2x+8-8\left(4\left(6-3x\right)^{2}-6\left(6-3x\right)+8\right)\right)$$

Combine 48x and -2x to get 46x.

$$5\left(x^{3}-12x^{2}+46x-64+8-8\left(4\left(6-3x\right)^{2}-6\left(6-3x\right)+8\right)\right)$$

Add -64 and 8 to get -56.

$$5\left(x^{3}-12x^{2}+46x-56-8\left(4\left(6-3x\right)^{2}-6\left(6-3x\right)+8\right)\right)$$

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

$$5\left(x^{3}-12x^{2}+46x-56-8\left(4\left(36-36x+9x^{2}\right)-6\left(6-3x\right)+8\right)\right)$$

Use the distributive property to multiply 4 by 36-36x+9x^{2}.

$$5\left(x^{3}-12x^{2}+46x-56-8\left(144-144x+36x^{2}-6\left(6-3x\right)+8\right)\right)$$

Use the distributive property to multiply -6 by 6-3x.

$$5\left(x^{3}-12x^{2}+46x-56-8\left(144-144x+36x^{2}-36+18x+8\right)\right)$$

Subtract 36 from 144 to get 108.

$$5\left(x^{3}-12x^{2}+46x-56-8\left(108-144x+36x^{2}+18x+8\right)\right)$$

Combine -144x and 18x to get -126x.

$$5\left(x^{3}-12x^{2}+46x-56-8\left(108-126x+36x^{2}+8\right)\right)$$

Add 108 and 8 to get 116.

$$5\left(x^{3}-12x^{2}+46x-56-8\left(116-126x+36x^{2}\right)\right)$$

Use the distributive property to multiply -8 by 116-126x+36x^{2}.

$$5\left(x^{3}-12x^{2}+46x-56-928+1008x-288x^{2}\right)$$

Subtract 928 from -56 to get -984.

$$5\left(x^{3}-12x^{2}+46x-984+1008x-288x^{2}\right)$$

Combine 46x and 1008x to get 1054x.

$$5\left(x^{3}-12x^{2}+1054x-984-288x^{2}\right)$$

Combine -12x^{2} and -288x^{2} to get -300x^{2}.

$$5\left(x^{3}-300x^{2}+1054x-984\right)$$

Use the distributive property to multiply 5 by x^{3}-300x^{2}+1054x-984.

$$5x^{3}-1500x^{2}+5270x-4920$$