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

The solution to expand (sqrt(x+1)-4sqrt(x))^3 is (x+1)sqrt(x+1)-76sqrt(x^3)-12sqrt(x)+48xsqrt(x+1)

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

expand

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

(x + 1) x + 1 - 76 x^{3} - 12 x + 48 x x + 1

Solution steps

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

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

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

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

Simplify

(x + 1)^{3} - 3 (x + 1)^{2} \cdot 4 x + 3 x + 1 (4 x)^{2} - (4 x)^{3} : (x + 1) x + 1 - 76 x^{\frac{3}{2}} - 12 x + 48 x x + 1

= (x + 1) x + 1 - 76 x^{\frac{3}{2}} - 12 x + 48 x x + 1

x^{\frac{3}{2}} = x^{3}

= (x + 1) x + 1 - 76 x^{3} - 12 x + 48 x x + 1

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

cos (2 (t - 1))

\frac{x ( x - 5 )}{( x + 3 ) ( x - 1 )}

\frac{9 x ^{2} ( x - 7 ) ^{2}}{( x + 5 ) ^{2}}

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

What is expand (sqrt(x+1)-4sqrt(x))^3 ?
The solution to expand (sqrt(x+1)-4sqrt(x))^3 is (x+1)sqrt(x+1)-76sqrt(x^3)-12sqrt(x)+48xsqrt(x+1)