Solve (2t-3)^2+(-2t+2)(5t+2)

$$( 2 t - 3 ) ^ { 2 } + ( - 2 t + 2 ) ( 5 t + 2 )$$

Evaluate

$$13-6t-6t^{2}$$

Solution Steps

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

$$4t^{2}-12t+9+\left(-2t+2\right)\left(5t+2\right)$$

Use the distributive property to multiply -2t+2 by 5t+2 and combine like terms.

$$4t^{2}-12t+9-10t^{2}+6t+4$$

Combine 4t^{2} and -10t^{2} to get -6t^{2}.

$$-6t^{2}-12t+9+6t+4$$

Combine -12t and 6t to get -6t.

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

Add 9 and 4 to get 13.

$$-6t^{2}-6t+13$$

Expand

$$13-6t-6t^{2}$$

Solution Steps

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

$$4t^{2}-12t+9+\left(-2t+2\right)\left(5t+2\right)$$

Use the distributive property to multiply -2t+2 by 5t+2 and combine like terms.

$$4t^{2}-12t+9-10t^{2}+6t+4$$

Combine 4t^{2} and -10t^{2} to get -6t^{2}.

$$-6t^{2}-12t+9+6t+4$$

Combine -12t and 6t to get -6t.

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

Add 9 and 4 to get 13.

$$-6t^{2}-6t+13$$