What is expand ((7+sqrt(4x+25))/2)^2 ?

The solution to expand ((7+sqrt(4x+25))/2)^2 is x+(7sqrt(4x+25))/2+37/2

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expand ((7+sqrt(4x+25))/2)^2

expand

(\frac{7 + 4 x + 25}{2})^{2}

x + \frac{7 4 x + 25}{2} + \frac{37}{2}

Solution steps

(\frac{7 + 4 x + 25}{2})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 7 + 4 x + 25 ) ^{2}}{2 ^{2}}

(7 + 4 x + 25)^{2} = 4 x + 14 4 x + 25 + 74

= \frac{4 x + 14 4 x + 25 + 74}{2 ^{2}}

Factor

4 x + 14 4 x + 25 + 74 : 2 (2 x + 7 25 + 4 x + 37)

= \frac{2 ( 2 x + 7 25 + 4 x + 37 )}{2 ^{2}}

Cancel the common factor:

2

= \frac{2 x + 7 4 x + 25 + 37}{2}

Apply the fraction rule:

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

\frac{2 x + 7 4 x + 25 + 37}{2} = \frac{2 x}{2} + \frac{7 4 x + 25}{2} + \frac{37}{2}

= \frac{2 x}{2} + \frac{7 4 x + 25}{2} + \frac{37}{2}

Divide the numbers:

\frac{2}{2} = 1

= x + \frac{7 4 x + 25}{2} + \frac{37}{2}

\frac{\partial}{\partial x} ((u) (a u + b v))

\frac{( b - 2 a ) ^{2}}{2}

895 \cdot 7

\frac{2 ( 1 - 4 k )}{3}

- \frac{( e ^{iπ x} - e ^{- iπ x} ) ^{2}}{4}

What is expand ((7+sqrt(4x+25))/2)^2 ?
The solution to expand ((7+sqrt(4x+25))/2)^2 is x+(7sqrt(4x+25))/2+37/2