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

The solution to expand sqrt(x+1)*(x+1)^2 is x^2sqrt(x+1)+2xsqrt(x+1)+sqrt(x+1)

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expand sqrt(x+1)*(x+1)^2

expand

x + 1 \cdot (x + 1)^{2}

x^{2} x + 1 + 2 x x + 1 + x + 1

Solution steps

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

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

Expand

(x + 1)^{2} : x^{2} + 2 x + 1

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

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

Apply the distributive law:

m (a + b + c) = ma + mb + m c

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

= x + 1 x^{2} + x + 1 \cdot 2 x + x + 1 \cdot 1

Simplify

x + 1 x^{2} + x + 1 \cdot 2 x + x + 1 \cdot 1 : x^{2} x + 1 + 2 x x + 1 + x + 1

= x^{2} x + 1 + 2 x x + 1 + x + 1

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

\frac{sec ^{2} ( \frac{π}{4} )}{2 tan ( \frac{π}{4} )}

x + 1 \cdot (x + 1)

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

(x - 3) (x + 1 - 5) (x + 1 + 5)

What is expand sqrt(x+1)*(x+1)^2 ?
The solution to expand sqrt(x+1)*(x+1)^2 is x^2sqrt(x+1)+2xsqrt(x+1)+sqrt(x+1)