What is expand (2dt+2dw)*(3dt-dw) ?

The solution to expand (2dt+2dw)*(3dt-dw) is 6dt^2+4dwdt-2dw^2

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expand (2dt+2dw)*(3dt-dw)

expand

(2 d t + 2 d w) \cdot (3 d t - d w)

6 d t^{2} + 4 d w d t - 2 d w^{2}

Solution steps

(2 d t + 2 d w) (3 d t - d w)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = 2 d t, b = 2 d w, c = 3 d t, d = - d w

= 2 d t \cdot 3 d t + 2 d t (- d w) + 2 d w \cdot 3 d t + 2 d w (- d w)

Apply minus-plus rules

+ (- a) = - a

= 2 \cdot 3 d t d t - 2 d t d w + 2 \cdot 3 d w d t - 2 d w d w

Simplify

2 \cdot 3 d t d t - 2 d t d w + 2 \cdot 3 d w d t - 2 d w d w : 6 d t^{2} + 4 d w d t - 2 d w^{2}

= 6 d t^{2} + 4 d w d t - 2 d w^{2}

\frac{( n + 1 ) ( 2 n + 1 )}{18 n}

F (s - π)

\frac{1}{2 ( x + h ) ^{2}}

\frac{( x ^{2} + 1 ) ^{2}}{x + 1}

ln (x - 1) (x - 2)

What is expand (2dt+2dw)*(3dt-dw) ?
The solution to expand (2dt+2dw)*(3dt-dw) is 6dt^2+4dwdt-2dw^2