Solve -{left(3t-3/2right)}^2+41/16

$$- { \left(3t- \frac{ 3 }{ 2 } \right) }^{ 2 } + \frac{ 41 }{ 16 }$$

Evaluate

$$-\frac{9\left(2t-1\right)^{2}}{4}+\frac{41}{16}$$

Solution Steps

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

$$-\left(9t^{2}-9t+\frac{9}{4}\right)+\frac{41}{16}$$

To find the opposite of 9t^{2}-9t+\frac{9}{4}, find the opposite of each term.

$$-9t^{2}+9t-\frac{9}{4}+\frac{41}{16}$$

Add -\frac{9}{4} and \frac{41}{16} to get \frac{5}{16}.

$$-9t^{2}+9t+\frac{5}{16}$$

Expand

$$\frac{5}{16}+9t-9t^{2}$$

Solution Steps

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

$$-\left(9t^{2}-9t+\frac{9}{4}\right)+\frac{41}{16}$$

To find the opposite of 9t^{2}-9t+\frac{9}{4}, find the opposite of each term.

$$-9t^{2}+9t-\frac{9}{4}+\frac{41}{16}$$

Add -\frac{9}{4} and \frac{41}{16} to get \frac{5}{16}.

$$-9t^{2}+9t+\frac{5}{16}$$