Solve (6x^{6}-12x^4)8x-(36x^5-48x^3*2x^8-8)

$$( 6 x ^ { 6 } - 12 x ^ { 4 } ) 8 x - ( 36 x ^ { 5 } - 48 x ^ { 3 } \cdot 2 x ^ { 8 } - 8 )$$

Evaluate

$$96x^{11}+48x^{7}-132x^{5}+8$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$\left(6x^{6}-12x^{4}\right)\times 8x-\left(36x^{5}-48x^{11}\times 2-8\right)$$

Use the distributive property to multiply 6x^{6}-12x^{4} by 8.

$$\left(48x^{6}-96x^{4}\right)x-\left(36x^{5}-48x^{11}\times 2-8\right)$$

Use the distributive property to multiply 48x^{6}-96x^{4} by x.

$$48x^{7}-96x^{5}-\left(36x^{5}-48x^{11}\times 2-8\right)$$

Multiply 48 and 2 to get 96.

$$48x^{7}-96x^{5}-\left(36x^{5}-96x^{11}-8\right)$$

To find the opposite of 36x^{5}-96x^{11}-8, find the opposite of each term.

$$48x^{7}-96x^{5}-36x^{5}+96x^{11}+8$$

Combine -96x^{5} and -36x^{5} to get -132x^{5}.

$$48x^{7}-132x^{5}+96x^{11}+8$$

Expand

$$96x^{11}+48x^{7}-132x^{5}+8$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$\left(6x^{6}-12x^{4}\right)\times 8x-\left(36x^{5}-48x^{11}\times 2-8\right)$$

Use the distributive property to multiply 6x^{6}-12x^{4} by 8.

$$\left(48x^{6}-96x^{4}\right)x-\left(36x^{5}-48x^{11}\times 2-8\right)$$

Use the distributive property to multiply 48x^{6}-96x^{4} by x.

$$48x^{7}-96x^{5}-\left(36x^{5}-48x^{11}\times 2-8\right)$$

Multiply 48 and 2 to get 96.

$$48x^{7}-96x^{5}-\left(36x^{5}-96x^{11}-8\right)$$

To find the opposite of 36x^{5}-96x^{11}-8, find the opposite of each term.

$$48x^{7}-96x^{5}-36x^{5}+96x^{11}+8$$

Combine -96x^{5} and -36x^{5} to get -132x^{5}.

$$48x^{7}-132x^{5}+96x^{11}+8$$