Solve 7m^2-1-[m^2+3n-(5-n)-(-3+m^2)]}-(2n+3)

$$7 m ^ { 2 } - 1 - [ m ^ { 2 } + 3 n - ( 5 - n ) - ( - 3 + m ^ { 2 } ) ] \} - ( 2 n + 3 )$$

Evaluate

$$7m^{2}-4n+1$$

Solution Steps

To find the opposite of 5-n, find the opposite of each term.

$$7m^{2}-1-\left(m^{2}+3n-5+n-\left(-3+m^{2}\right)\right)$$

Combine 3n and n to get 4n.

$$7m^{2}-1-\left(m^{2}+4n-5-\left(-3+m^{2}\right)\right)$$

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

$$7m^{2}-1-\left(m^{2}+4n-5+3-m^{2}\right)$$

Add -5 and 3 to get -2.

$$7m^{2}-1-\left(m^{2}+4n-2-m^{2}\right)$$

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

$$7m^{2}-1-\left(4n-2\right)$$

To find the opposite of 4n-2, find the opposite of each term.

$$7m^{2}-1-4n+2$$

Add -1 and 2 to get 1.

$$7m^{2}+1-4n$$

Expand

$$7m^{2}-4n+1$$

Solution Steps

To find the opposite of 5-n, find the opposite of each term.

$$7m^{2}-1-\left(m^{2}+3n-5+n-\left(-3+m^{2}\right)\right)$$

Combine 3n and n to get 4n.

$$7m^{2}-1-\left(m^{2}+4n-5-\left(-3+m^{2}\right)\right)$$

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

$$7m^{2}-1-\left(m^{2}+4n-5+3-m^{2}\right)$$

Add -5 and 3 to get -2.

$$7m^{2}-1-\left(m^{2}+4n-2-m^{2}\right)$$

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

$$7m^{2}-1-\left(4n-2\right)$$

To find the opposite of 4n-2, find the opposite of each term.

$$7m^{2}-1-4n+2$$

Add -1 and 2 to get 1.

$$7m^{2}+1-4n$$