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

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

Evaluate

$$13x^{4}+5x^{3}-11x^{2}-6x+1$$

Solution Steps

To find the opposite of -7x^{4}-5x^{3}+7x^{2}, find the opposite of each term.

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

Combine 6x^{4} and 7x^{4} to get 13x^{4}.

$$13x^{4}-2x^{2}+6+5x^{3}-7x^{2}-\left(2x^{2}+6x+5\right)$$

Combine -2x^{2} and -7x^{2} to get -9x^{2}.

$$13x^{4}-9x^{2}+6+5x^{3}-\left(2x^{2}+6x+5\right)$$

To find the opposite of 2x^{2}+6x+5, find the opposite of each term.

$$13x^{4}-9x^{2}+6+5x^{3}-2x^{2}-6x-5$$

Combine -9x^{2} and -2x^{2} to get -11x^{2}.

$$13x^{4}-11x^{2}+6+5x^{3}-6x-5$$

Subtract 5 from 6 to get 1.

$$13x^{4}-11x^{2}+1+5x^{3}-6x$$

Expand

$$13x^{4}+5x^{3}-11x^{2}-6x+1$$

Solution Steps

To find the opposite of -7x^{4}-5x^{3}+7x^{2}, find the opposite of each term.

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

Combine 6x^{4} and 7x^{4} to get 13x^{4}.

$$13x^{4}-2x^{2}+6+5x^{3}-7x^{2}-\left(2x^{2}+6x+5\right)$$

Combine -2x^{2} and -7x^{2} to get -9x^{2}.

$$13x^{4}-9x^{2}+6+5x^{3}-\left(2x^{2}+6x+5\right)$$

To find the opposite of 2x^{2}+6x+5, find the opposite of each term.

$$13x^{4}-9x^{2}+6+5x^{3}-2x^{2}-6x-5$$

Combine -9x^{2} and -2x^{2} to get -11x^{2}.

$$13x^{4}-11x^{2}+6+5x^{3}-6x-5$$

Subtract 5 from 6 to get 1.

$$13x^{4}-11x^{2}+1+5x^{3}-6x$$