Solve (t+3)^2-(-2t-1)(1-2t)

$$( t + 3 ) ^ { 2 } - ( - 2 t - 1 ) ( 1 - 2 t )$$

Evaluate

$$10+6t-3t^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(t+3\right)^{2}.

$$t^{2}+6t+9-\left(-2t-1\right)\left(1-2t\right)$$

Use the distributive property to multiply -2t-1 by 1-2t and combine like terms.

$$t^{2}+6t+9-\left(4t^{2}-1\right)$$

To find the opposite of 4t^{2}-1, find the opposite of each term.

$$t^{2}+6t+9-4t^{2}+1$$

Combine t^{2} and -4t^{2} to get -3t^{2}.

$$-3t^{2}+6t+9+1$$

Add 9 and 1 to get 10.

$$-3t^{2}+6t+10$$

Expand

$$10+6t-3t^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(t+3\right)^{2}.

$$t^{2}+6t+9-\left(-2t-1\right)\left(1-2t\right)$$

Use the distributive property to multiply -2t-1 by 1-2t and combine like terms.

$$t^{2}+6t+9-\left(4t^{2}-1\right)$$

To find the opposite of 4t^{2}-1, find the opposite of each term.

$$t^{2}+6t+9-4t^{2}+1$$

Combine t^{2} and -4t^{2} to get -3t^{2}.

$$-3t^{2}+6t+9+1$$

Add 9 and 1 to get 10.

$$-3t^{2}+6t+10$$