Solve -(1-4(n+n)(1+4(m+n))

$$- ( 1 - 4 ( n + n ) ( 1 + 4 ( m + n ) )$$

Evaluate

$$-\left(-8n\left(4m+4n+1\right)+1\right)$$

Solution Steps

Combine n and n to get 2n.

$$-\left(1-4\times 2n\left(1+4\left(m+n\right)\right)\right)$$

Multiply 4 and 2 to get 8.

$$-\left(1-8n\left(1+4\left(m+n\right)\right)\right)$$

Use the distributive property to multiply 4 by m+n.

$$-\left(1-8n\left(1+4m+4n\right)\right)$$

Use the distributive property to multiply -8n by 1+4m+4n.

$$-\left(1-8n-32nm-32n^{2}\right)$$

To find the opposite of 1-8n-32nm-32n^{2}, find the opposite of each term.

$$-1-\left(-8n\right)-\left(-32nm\right)-\left(-32n^{2}\right)$$

The opposite of -8n is 8n.

$$-1+8n-\left(-32nm\right)-\left(-32n^{2}\right)$$

The opposite of -32nm is 32nm.

$$-1+8n+32nm-\left(-32n^{2}\right)$$

The opposite of -32n^{2} is 32n^{2}.

$$-1+8n+32nm+32n^{2}$$

Expand

$$32mn+32n^{2}+8n-1$$

Solution Steps

Combine n and n to get 2n.

$$-\left(1-4\times 2n\left(1+4\left(m+n\right)\right)\right)$$

Multiply 4 and 2 to get 8.

$$-\left(1-8n\left(1+4\left(m+n\right)\right)\right)$$

Use the distributive property to multiply 4 by m+n.

$$-\left(1-8n\left(1+4m+4n\right)\right)$$

Use the distributive property to multiply -8n by 1+4m+4n.

$$-\left(1-8n-32nm-32n^{2}\right)$$

To find the opposite of 1-8n-32nm-32n^{2}, find the opposite of each term.

$$-1-\left(-8n\right)-\left(-32nm\right)-\left(-32n^{2}\right)$$

The opposite of -8n is 8n.

$$-1+8n-\left(-32nm\right)-\left(-32n^{2}\right)$$

The opposite of -32nm is 32nm.

$$-1+8n+32nm-\left(-32n^{2}\right)$$

The opposite of -32n^{2} is 32n^{2}.

$$-1+8n+32nm+32n^{2}$$