Solve (x^3+8x^2)^2(x-8)

$$( x ^ { 3 } + 8 x ^ { 2 } ) ^ { 2 } ( x - 8 )$$

Evaluate

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

Solution Steps

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

$$\left(\left(x^{3}\right)^{2}+16x^{3}x^{2}+64\left(x^{2}\right)^{2}\right)\left(x-8\right)$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\left(x^{6}+16x^{3}x^{2}+64\left(x^{2}\right)^{2}\right)\left(x-8\right)$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\left(x^{6}+16x^{5}+64\left(x^{2}\right)^{2}\right)\left(x-8\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(x^{6}+16x^{5}+64x^{4}\right)\left(x-8\right)$$

Use the distributive property to multiply x^{6}+16x^{5}+64x^{4} by x-8 and combine like terms.

$$x^{7}+8x^{6}-64x^{5}-512x^{4}$$

Expand

$$x^{7}+8x^{6}-64x^{5}-512x^{4}$$

Solution Steps

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

$$\left(\left(x^{3}\right)^{2}+16x^{3}x^{2}+64\left(x^{2}\right)^{2}\right)\left(x-8\right)$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\left(x^{6}+16x^{3}x^{2}+64\left(x^{2}\right)^{2}\right)\left(x-8\right)$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\left(x^{6}+16x^{5}+64\left(x^{2}\right)^{2}\right)\left(x-8\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(x^{6}+16x^{5}+64x^{4}\right)\left(x-8\right)$$

Use the distributive property to multiply x^{6}+16x^{5}+64x^{4} by x-8 and combine like terms.

$$x^{7}+8x^{6}-64x^{5}-512x^{4}$$