Solve (2-t)^2+(2-t)b+c

$$( 2 - t ) ^ { 2 } + ( 2 - t ) b + c$$

Evaluate

$$b\left(2-t\right)+\left(2-t\right)^{2}+c$$

Solution Steps

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

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

Use the distributive property to multiply 2-t by b.

$$4-4t+t^{2}+2b-tb+c$$

Expand

$$t^{2}-bt-4t+c+2b+4$$

Solution Steps

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

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

Use the distributive property to multiply 2-t by b.

$$4-4t+t^{2}+2b-tb+c$$