What is expand (1/6 d-1/3 q)^2 ?

The solution to expand (1/6 d-1/3 q)^2 is (d^2-4dq+4q^2)/(36)

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expand (1/6 d-1/3 q)^2

expand

(\frac{1}{6} d - \frac{1}{3} q)^{2}

\frac{d ^{2} - 4 d q + 4 q ^{2}}{36}

Solution steps

(\frac{1}{6} d - \frac{1}{3} q)^{2}

Apply Perfect Square Formula:

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

(\frac{1}{6} d - \frac{1}{3} q)^{2} = (\frac{1}{6} d)^{2} - 2 \cdot \frac{1}{6} d \frac{1}{3} q + (\frac{1}{3} q)^{2}

= (\frac{1}{6} d)^{2} - 2 \cdot \frac{1}{6} d \frac{1}{3} q + (\frac{1}{3} q)^{2}

Simplify

(\frac{1}{6} d)^{2} - 2 \cdot \frac{1}{6} d \frac{1}{3} q + (\frac{1}{3} q)^{2} : \frac{d ^{2} - 4 d q + 4 q ^{2}}{36}

= \frac{d ^{2} - 4 d q + 4 q ^{2}}{36}

\frac{( 0.5 + x ) ( 0.4 + x )}{( 0.5 - x ) ( 0.45 - x )}

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\frac{10 ( 694 - 1 )}{231}

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What is expand (1/6 d-1/3 q)^2 ?
The solution to expand (1/6 d-1/3 q)^2 is (d^2-4dq+4q^2)/(36)