What is expand ((tx+t)^2)/4 ?

The solution to expand ((tx+t)^2)/4 is (t^2x^2)/4+(t^2x)/2+(t^2)/4

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expand ((tx+t)^2)/4

expand

\frac{( t x + t ) ^{2}}{4}

\frac{t ^{2} x ^{2}}{4} + \frac{t ^{2} x}{2} + \frac{t ^{2}}{4}

Solution steps

\frac{( t x + t ) ^{2}}{4}

(t x + t)^{2} = t^{2} x^{2} + 2 t^{2} x + t^{2}

= \frac{t ^{2} x ^{2} + 2 t ^{2} x + t ^{2}}{4}

Apply the fraction rule:

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

\frac{t ^{2} x ^{2} + 2 t ^{2} x + t ^{2}}{4} = \frac{t ^{2} x ^{2}}{4} + \frac{2 t ^{2} x}{4} + \frac{t ^{2}}{4}

= \frac{t ^{2} x ^{2}}{4} + \frac{2 t ^{2} x}{4} + \frac{t ^{2}}{4}

Cancel

\frac{2 t ^{2} x}{4} : \frac{t ^{2} x}{2}

= \frac{t ^{2} x ^{2}}{4} + \frac{t ^{2} x}{2} + \frac{t ^{2}}{4}

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What is expand ((tx+t)^2)/4 ?
The solution to expand ((tx+t)^2)/4 is (t^2x^2)/4+(t^2x)/2+(t^2)/4