Solve 4bc-(3b^{2}c-5bc^{2})-[2b^2c-(7bc-3bc^2)+8bc-5b^2c]-2bc^2

$$4 b c - ( 3 b ^ { 2 } c - 5 b c ^ { 2 } ) - [ 2 b ^ { 2 } c - ( 7 b c - 3 b c ^ { 2 } ) + 8 b c - 5 b ^ { 2 } c ] - 2 b c ^ { 2 }$$

Evaluate

$$3bc$$

Solution Steps

Multiply -1 and 5 to get -5.

$$4bc-\left(3b^{2}c-5bc^{2}\right)-\left(2b^{2}c-\left(7bc-3bc^{2}\right)+8bc-5b^{2}c\right)-2bc^{2}$$

To find the opposite of 3b^{2}c-5bc^{2}, find the opposite of each term.

$$4bc-3b^{2}c+5bc^{2}-\left(2b^{2}c-\left(7bc-3bc^{2}\right)+8bc-5b^{2}c\right)-2bc^{2}$$

To find the opposite of 7bc-3bc^{2}, find the opposite of each term.

$$4bc-3b^{2}c+5bc^{2}-\left(2b^{2}c-7bc+3bc^{2}+8bc-5b^{2}c\right)-2bc^{2}$$

Combine -7bc and 8bc to get bc.

$$4bc-3b^{2}c+5bc^{2}-\left(2b^{2}c+bc+3bc^{2}-5b^{2}c\right)-2bc^{2}$$

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

$$4bc-3b^{2}c+5bc^{2}-\left(-3b^{2}c+bc+3bc^{2}\right)-2bc^{2}$$

To find the opposite of -3b^{2}c+bc+3bc^{2}, find the opposite of each term.

$$4bc-3b^{2}c+5bc^{2}+3b^{2}c-bc-3bc^{2}-2bc^{2}$$

Combine -3b^{2}c and 3b^{2}c to get 0.

$$4bc+5bc^{2}-bc-3bc^{2}-2bc^{2}$$

Combine 4bc and -bc to get 3bc.

$$3bc+5bc^{2}-3bc^{2}-2bc^{2}$$

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

$$3bc+2bc^{2}-2bc^{2}$$

Combine 2bc^{2} and -2bc^{2} to get 0.

$$3bc$$

Expand

$$3bc$$

Solution Steps

Multiply -1 and 5 to get -5.

$$4bc-\left(3b^{2}c-5bc^{2}\right)-\left(2b^{2}c-\left(7bc-3bc^{2}\right)+8bc-5b^{2}c\right)-2bc^{2}$$

To find the opposite of 3b^{2}c-5bc^{2}, find the opposite of each term.

$$4bc-3b^{2}c+5bc^{2}-\left(2b^{2}c-\left(7bc-3bc^{2}\right)+8bc-5b^{2}c\right)-2bc^{2}$$

To find the opposite of 7bc-3bc^{2}, find the opposite of each term.

$$4bc-3b^{2}c+5bc^{2}-\left(2b^{2}c-7bc+3bc^{2}+8bc-5b^{2}c\right)-2bc^{2}$$

Combine -7bc and 8bc to get bc.

$$4bc-3b^{2}c+5bc^{2}-\left(2b^{2}c+bc+3bc^{2}-5b^{2}c\right)-2bc^{2}$$

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

$$4bc-3b^{2}c+5bc^{2}-\left(-3b^{2}c+bc+3bc^{2}\right)-2bc^{2}$$

To find the opposite of -3b^{2}c+bc+3bc^{2}, find the opposite of each term.

$$4bc-3b^{2}c+5bc^{2}+3b^{2}c-bc-3bc^{2}-2bc^{2}$$

Combine -3b^{2}c and 3b^{2}c to get 0.

$$4bc+5bc^{2}-bc-3bc^{2}-2bc^{2}$$

Combine 4bc and -bc to get 3bc.

$$3bc+5bc^{2}-3bc^{2}-2bc^{2}$$

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

$$3bc+2bc^{2}-2bc^{2}$$

Combine 2bc^{2} and -2bc^{2} to get 0.

$$3bc$$