Solve (15ab-3a^2)+(6a^2-12ab+c)-(5a^2+c+3ab)

$$( 15 a b - 3 a ^ { 2 } ) + ( 6 a ^ { 2 } - 12 a b + c ) - ( 5 a ^ { 2 } + c + 3 a b )$$

Evaluate

$$-2a^{2}$$

Solution Steps

Combine -3a^{2} and 6a^{2} to get 3a^{2}.

$$15ab+3a^{2}-12ab+c-\left(5a^{2}+c+3ab\right)$$

Combine 15ab and -12ab to get 3ab.

$$3ab+3a^{2}+c-\left(5a^{2}+c+3ab\right)$$

To find the opposite of 5a^{2}+c+3ab, find the opposite of each term.

$$3ab+3a^{2}+c-5a^{2}-c-3ab$$

Combine 3a^{2} and -5a^{2} to get -2a^{2}.

$$3ab-2a^{2}+c-c-3ab$$

Combine c and -c to get 0.

$$3ab-2a^{2}-3ab$$

Combine 3ab and -3ab to get 0.

$$-2a^{2}$$

Expand

$$-2a^{2}$$

Solution Steps

Combine -3a^{2} and 6a^{2} to get 3a^{2}.

$$15ab+3a^{2}-12ab+c-\left(5a^{2}+c+3ab\right)$$

Combine 15ab and -12ab to get 3ab.

$$3ab+3a^{2}+c-\left(5a^{2}+c+3ab\right)$$

To find the opposite of 5a^{2}+c+3ab, find the opposite of each term.

$$3ab+3a^{2}+c-5a^{2}-c-3ab$$

Combine 3a^{2} and -5a^{2} to get -2a^{2}.

$$3ab-2a^{2}+c-c-3ab$$

Combine c and -c to get 0.

$$3ab-2a^{2}-3ab$$

Combine 3ab and -3ab to get 0.

$$-2a^{2}$$