What is expand 2((x+7)/4)^2 ?

The solution to expand 2((x+7)/4)^2 is (x^2)/8+(7x)/4+49/8

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expand 2((x+7)/4)^2

expand

2 (\frac{x + 7}{4})^{2}

\frac{x ^{2}}{8} + \frac{7 x}{4} + \frac{49}{8}

Solution steps

2 (\frac{x + 7}{4})^{2}

(\frac{x + 7}{4})^{2} = \frac{x ^{2} + 14 x + 49}{4 ^{2}}

= 2 \cdot \frac{x ^{2} + 14 x + 49}{4 ^{2}}

Multiply fractions:

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

= \frac{( x ^{2} + 14 x + 49 ) \cdot 2}{4 ^{2}}

Factor

4^{2} : 2^{4}

= \frac{2 ( x ^{2} + 14 x + 49 )}{2 ^{4}}

Cancel the common factor:

2

= \frac{x ^{2} + 14 x + 49}{2 ^{3}}

2^{3} = 8

= \frac{x ^{2} + 14 x + 49}{8}

Apply the fraction rule:

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

\frac{x ^{2} + 14 x + 49}{8} = \frac{x ^{2}}{8} + \frac{14 x}{8} + \frac{49}{8}

= \frac{x ^{2}}{8} + \frac{14 x}{8} + \frac{49}{8}

Cancel

\frac{14 x}{8} : \frac{7 x}{4}

= \frac{x ^{2}}{8} + \frac{7 x}{4} + \frac{49}{8}

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

\frac{2 x - 1}{x ( x - 1 )}

(x + 2 y - 6 z)^{5}

(d - 3) (2 e + 4)

\frac{a \cdot x}{z \cdot ( 4 - x )}

What is expand 2((x+7)/4)^2 ?
The solution to expand 2((x+7)/4)^2 is (x^2)/8+(7x)/4+49/8