Solve (3x^{4}+5)-(-x^4-10)+(3x^2-7x-5)-(-6x^4+x^5)

$$( 3 x ^ { 4 } + 5 ) - ( - x ^ { 4 } - 10 ) + ( 3 x ^ { 2 } - 7 x - 5 ) - ( - 6 x ^ { 4 } + x ^ { 5 } )$$

Evaluate

$$10-7x+3x^{2}+10x^{4}-x^{5}$$

Solution Steps

To find the opposite of -x^{4}-10, find the opposite of each term.

$$3x^{4}+5-\left(-x^{4}\right)+10+3x^{2}-7x-5-\left(-6x^{4}+x^{5}\right)$$

Add 5 and 10 to get 15.

$$3x^{4}+15-\left(-x^{4}\right)+3x^{2}-7x-5-\left(-6x^{4}+x^{5}\right)$$

Subtract 5 from 15 to get 10.

$$3x^{4}+10-\left(-x^{4}\right)+3x^{2}-7x-\left(-6x^{4}+x^{5}\right)$$

To find the opposite of -6x^{4}+x^{5}, find the opposite of each term.

$$3x^{4}+10-\left(-x^{4}\right)+3x^{2}-7x+6x^{4}-x^{5}$$

Combine 3x^{4} and 6x^{4} to get 9x^{4}.

$$9x^{4}+10-\left(-x^{4}\right)+3x^{2}-7x-x^{5}$$

Multiply -1 and -1 to get 1.

$$9x^{4}+10+x^{4}+3x^{2}-7x-x^{5}$$

Combine 9x^{4} and x^{4} to get 10x^{4}.

$$10x^{4}+10+3x^{2}-7x-x^{5}$$

Expand

$$10-7x+3x^{2}+10x^{4}-x^{5}$$

Solution Steps

To find the opposite of -x^{4}-10, find the opposite of each term.

$$3x^{4}+5-\left(-x^{4}\right)+10+3x^{2}-7x-5-\left(-6x^{4}+x^{5}\right)$$

Add 5 and 10 to get 15.

$$3x^{4}+15-\left(-x^{4}\right)+3x^{2}-7x-5-\left(-6x^{4}+x^{5}\right)$$

Subtract 5 from 15 to get 10.

$$3x^{4}+10-\left(-x^{4}\right)+3x^{2}-7x-\left(-6x^{4}+x^{5}\right)$$

To find the opposite of -6x^{4}+x^{5}, find the opposite of each term.

$$3x^{4}+10-\left(-x^{4}\right)+3x^{2}-7x+6x^{4}-x^{5}$$

Combine 3x^{4} and 6x^{4} to get 9x^{4}.

$$9x^{4}+10-\left(-x^{4}\right)+3x^{2}-7x-x^{5}$$

Multiply -1 and -1 to get 1.

$$9x^{4}+10+x^{4}+3x^{2}-7x-x^{5}$$

Combine 9x^{4} and x^{4} to get 10x^{4}.

$$10x^{4}+10+3x^{2}-7x-x^{5}$$