What is expand (dt+3t^4dw)^2 ?

The solution to expand (dt+3t^4dw)^2 is dt^2+6t^4dtdw+9t^8dw^2

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expand (dt+3t^4dw)^2

expand

(d t + 3 t^{4} d w)^{2}

d t^{2} + 6 t^{4} d t d w + 9 t^{8} d w^{2}

Solution steps

(d t + 3 t^{4} d w)^{2}

Apply Perfect Square Formula:

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

a = d t, b = 3 t^{4} d w

= d t^{2} + 2 d t \cdot 3 t^{4} d w + (3 t^{4} d w)^{2}

Simplify

d t^{2} + 2 d t \cdot 3 t^{4} d w + (3 t^{4} d w)^{2} : d t^{2} + 6 t^{4} d t d w + 9 t^{8} d w^{2}

= d t^{2} + 6 t^{4} d t d w + 9 t^{8} d w^{2}

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What is expand (dt+3t^4dw)^2 ?
The solution to expand (dt+3t^4dw)^2 is dt^2+6t^4dtdw+9t^8dw^2