Solve 2t-{7-2[t-t(4+t)]}

$$2 t - \{ 7 - 2 [ t - t ( 4 + t ) ] \}$$

Evaluate

$$-2t^{2}-4t-7$$

Solution Steps

Use the distributive property to multiply t by 4+t.

$$2t-\left(7-2\left(t-\left(4t+t^{2}\right)\right)\right)$$

To find the opposite of 4t+t^{2}, find the opposite of each term.

$$2t-\left(7-2\left(t-4t-t^{2}\right)\right)$$

Combine t and -4t to get -3t.

$$2t-\left(7-2\left(-3t-t^{2}\right)\right)$$

Use the distributive property to multiply -2 by -3t-t^{2}.

$$2t-\left(7+6t+2t^{2}\right)$$

To find the opposite of 7+6t+2t^{2}, find the opposite of each term.

$$2t-7-6t-2t^{2}$$

Combine 2t and -6t to get -4t.

$$-4t-7-2t^{2}$$

Expand

$$-2t^{2}-4t-7$$

Solution Steps

Use the distributive property to multiply t by 4+t.

$$2t-\left(7-2\left(t-\left(4t+t^{2}\right)\right)\right)$$

To find the opposite of 4t+t^{2}, find the opposite of each term.

$$2t-\left(7-2\left(t-4t-t^{2}\right)\right)$$

Combine t and -4t to get -3t.

$$2t-\left(7-2\left(-3t-t^{2}\right)\right)$$

Use the distributive property to multiply -2 by -3t-t^{2}.

$$2t-\left(7+6t+2t^{2}\right)$$

To find the opposite of 7+6t+2t^{2}, find the opposite of each term.

$$2t-7-6t-2t^{2}$$

Combine 2t and -6t to get -4t.

$$-4t-7-2t^{2}$$