What is expand ((-t^2+20t-62)^2)/4 ?

The solution to expand ((-t^2+20t-62)^2)/4 is (t^4)/4-10t^3+131t^2-620t+961

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expand ((-t^2+20t-62)^2)/4

expand

\frac{( - t ^{2} + 20 t - 62 ) ^{2}}{4}

\frac{t ^{4}}{4} - 10 t^{3} + 131 t^{2} - 620 t + 961

Solution steps

\frac{( - t ^{2} + 20 t - 62 ) ^{2}}{4}

(- t^{2} + 20 t - 62)^{2} = t^{4} - 40 t^{3} + 524 t^{2} - 2480 t + 3844

= \frac{t ^{4} - 40 t ^{3} + 524 t ^{2} - 2480 t + 3844}{4}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{t ^{4} - 40 t ^{3} + 524 t ^{2} - 2480 t + 3844}{4} = \frac{t ^{4}}{4} - \frac{40 t ^{3}}{4} + \frac{524 t ^{2}}{4} - \frac{2480 t}{4} + \frac{3844}{4}

= \frac{t ^{4}}{4} - \frac{40 t ^{3}}{4} + \frac{524 t ^{2}}{4} - \frac{2480 t}{4} + \frac{3844}{4}

\frac{40 t ^{3}}{4} = 10 t^{3}

\frac{524 t ^{2}}{4} = 131 t^{2}

\frac{2480 t}{4} = 620 t

\frac{3844}{4} = 961

= \frac{t ^{4}}{4} - 10 t^{3} + 131 t^{2} - 620 t + 961

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What is expand ((-t^2+20t-62)^2)/4 ?
The solution to expand ((-t^2+20t-62)^2)/4 is (t^4)/4-10t^3+131t^2-620t+961