Solve =(2-8x)^3-7(2-8x)^2+5(2-8x)-1

$$= ( 2 - 8 x ) ^ { 3 } - 7 ( 2 - 8 x ) ^ { 2 } + 5 ( 2 - 8 x ) - 1$$

Evaluate

$$-512x^{3}-64x^{2}+88x-11$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2-8x\right)^{3}.

$$8-96x+384x^{2}-512x^{3}-7\left(2-8x\right)^{2}+5\left(2-8x\right)-1$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2-8x\right)^{2}.

$$8-96x+384x^{2}-512x^{3}-7\left(4-32x+64x^{2}\right)+5\left(2-8x\right)-1$$

Use the distributive property to multiply -7 by 4-32x+64x^{2}.

$$8-96x+384x^{2}-512x^{3}-28+224x-448x^{2}+5\left(2-8x\right)-1$$

Subtract 28 from 8 to get -20.

$$-20-96x+384x^{2}-512x^{3}+224x-448x^{2}+5\left(2-8x\right)-1$$

Combine -96x and 224x to get 128x.

$$-20+128x+384x^{2}-512x^{3}-448x^{2}+5\left(2-8x\right)-1$$

Combine 384x^{2} and -448x^{2} to get -64x^{2}.

$$-20+128x-64x^{2}-512x^{3}+5\left(2-8x\right)-1$$

Use the distributive property to multiply 5 by 2-8x.

$$-20+128x-64x^{2}-512x^{3}+10-40x-1$$

Add -20 and 10 to get -10.

$$-10+128x-64x^{2}-512x^{3}-40x-1$$

Combine 128x and -40x to get 88x.

$$-10+88x-64x^{2}-512x^{3}-1$$

Subtract 1 from -10 to get -11.

$$-11+88x-64x^{2}-512x^{3}$$

Expand

$$-512x^{3}-64x^{2}+88x-11$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2-8x\right)^{3}.

$$8-96x+384x^{2}-512x^{3}-7\left(2-8x\right)^{2}+5\left(2-8x\right)-1$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2-8x\right)^{2}.

$$8-96x+384x^{2}-512x^{3}-7\left(4-32x+64x^{2}\right)+5\left(2-8x\right)-1$$

Use the distributive property to multiply -7 by 4-32x+64x^{2}.

$$8-96x+384x^{2}-512x^{3}-28+224x-448x^{2}+5\left(2-8x\right)-1$$

Subtract 28 from 8 to get -20.

$$-20-96x+384x^{2}-512x^{3}+224x-448x^{2}+5\left(2-8x\right)-1$$

Combine -96x and 224x to get 128x.

$$-20+128x+384x^{2}-512x^{3}-448x^{2}+5\left(2-8x\right)-1$$

Combine 384x^{2} and -448x^{2} to get -64x^{2}.

$$-20+128x-64x^{2}-512x^{3}+5\left(2-8x\right)-1$$

Use the distributive property to multiply 5 by 2-8x.

$$-20+128x-64x^{2}-512x^{3}+10-40x-1$$

Add -20 and 10 to get -10.

$$-10+128x-64x^{2}-512x^{3}-40x-1$$

Combine 128x and -40x to get 88x.

$$-10+88x-64x^{2}-512x^{3}-1$$

Subtract 1 from -10 to get -11.

$$-11+88x-64x^{2}-512x^{3}$$