What is expand 2(sqrt(3)u-sqrt(3/7)v)^2 ?

The solution to expand 2(sqrt(3)u-sqrt(3/7)v)^2 is (2(21u^2-14sqrt(3)sqrt(3/7)uv+3v^2))/7

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expand 2(sqrt(3)u-sqrt(3/7)v)^2

expand

2 (3 u - \frac{3}{7} v)^{2}

\frac{2 ( 21 u ^{2} - 14 3 \frac{3}{7} uv + 3 v ^{2} )}{7}

Solution steps

2 (3 u - \frac{3}{7} v)^{2}

Apply Perfect Square Formula:

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

(3 u - \frac{3}{7} v)^{2} = (3 u)^{2} - 23 u \frac{3}{7} v + (\frac{3}{7} v)^{2}

= 2 (3 u)^{2} - 23 u \frac{3}{7} v + (\frac{3}{7} v)^{2}

Simplify

(3 u)^{2} - 23 u \frac{3}{7} v + (\frac{3}{7} v)^{2} : \frac{21 u ^{2} - 14 3 \frac{3}{7} uv + 3 v ^{2}}{7}

= 2 \cdot \frac{21 u ^{2} - 14 3 \frac{3}{7} uv + 3 v ^{2}}{7}

Apply the fraction rule:

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

= \frac{2 ( 21 u ^{2} - 14 3 \frac{3}{7} uv + 3 v ^{2} )}{7}

\frac{4 h ^{2}}{( 12 h ^{2} - 8 h + 1 ) ( 3 h + 1 )}

lo g_{10} (3) (x^{2} - 1)

\frac{e ^{- 7 x} - 2 x + 6}{( x - 3 ) ( x - 1 )}

sin (2^{(k + 2)} x)

What is expand 2(sqrt(3)u-sqrt(3/7)v)^2 ?
The solution to expand 2(sqrt(3)u-sqrt(3/7)v)^2 is (2(21u^2-14sqrt(3)sqrt(3/7)uv+3v^2))/7