What is expand (dt+t^7dw)^2 ?

The solution to expand (dt+t^7dw)^2 is dt^2+2t^7dtdw+t^{14}dw^2

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expand (dt+t^7dw)^2

expand

(d t + t^{7} d w)^{2}

d t^{2} + 2 t^{7} d t d w + t^{14} d w^{2}

Solution steps

(d t + t^{7} d w)^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = d t, b = t^{7} d w

= d t^{2} + 2 d t t^{7} d w + (t^{7} d w)^{2}

(t^{7} d w)^{2} = t^{14} d w^{2}

= d t^{2} + 2 t^{7} d t d w + t^{14} d w^{2}

(- 14, - 6) y (- 12 y^{22})

(4 x^{3} y - 15 x^{2} - y) d x

(1 + 8 (2 x^{2} - x))

(3 y d x + 6 d x - x d y = 0) \frac{1}{x d x}

2 (x^{2} + 4 x + 8)^{2}

What is expand (dt+t^7dw)^2 ?
The solution to expand (dt+t^7dw)^2 is dt^2+2t^7dtdw+t^{14}dw^2