What is expand (3x+4sqrt(x+1)+1)^2 ?

The solution to expand (3x+4sqrt(x+1)+1)^2 is 9x^2+22x+24xsqrt(x+1)+8sqrt(x+1)+17

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expand (3x+4sqrt(x+1)+1)^2

expand

(3 x + 4 x + 1 + 1)^{2}

9 x^{2} + 22 x + 24 x x + 1 + 8 x + 1 + 17

Solution steps

(3 x + 4 x + 1 + 1)^{2}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(3 x + 4 x + 1 + 1)^{2} = (3 x + 4 x + 1 + 1) (3 x + 4 x + 1 + 1)

= (3 x + 4 x + 1 + 1) (3 x + 4 x + 1 + 1)

Distribute parentheses

= 3 x \cdot 3 x + 3 x \cdot 4 x + 1 + 3 x \cdot 1 + 4 x + 1 \cdot 3 x + 4 x + 1 \cdot 4 x + 1 + 4 x + 1 \cdot 1 + 1 \cdot 3 x + 1 \cdot 4 x + 1 + 1 \cdot 1

Simplify

3 x \cdot 3 x + 3 x \cdot 4 x + 1 + 3 x \cdot 1 + 4 x + 1 \cdot 3 x + 4 x + 1 \cdot 4 x + 1 + 4 x + 1 \cdot 1 + 1 \cdot 3 x + 1 \cdot 4 x + 1 + 1 \cdot 1 : 9 x^{2} + 22 x + 24 x x + 1 + 8 x + 1 + 17

= 9 x^{2} + 22 x + 24 x x + 1 + 8 x + 1 + 17

(\frac{12}{25}) \cdot (\frac{- 4}{5})

\frac{( x - 5 ) ( x ^{2} + 5 x + 4 )}{x ^{2} - 2 x - 8}

2 p 1 + x^{2} + p (50 - x)

9 e^{2} x (20 x^{2} + 5)

(F \cdot x - \frac{F \cdot L \cdot x}{a}) \cdot (x - \frac{L \cdot x}{a})

What is expand (3x+4sqrt(x+1)+1)^2 ?
The solution to expand (3x+4sqrt(x+1)+1)^2 is 9x^2+22x+24xsqrt(x+1)+8sqrt(x+1)+17