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

The solution to x*sqrt(x^3+3x^2+3x+1) is xsqrt(x+1)(x+1)

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simplify x*sqrt(x^3+3x^2+3x+1)

simplify

x \cdot x^{3} + 3 x^{2} + 3 x + 1

x x + 1 (x + 1)

Solution steps

x x^{3} + 3 x^{2} + 3 x + 1

Factor

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

= x (x + 1)^{3}

Apply exponent rule:

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

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

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

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

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

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

Apply radical rule:

a^{2} = a,

assuming

a \geq 0

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

= x (x + 1) x + 1

= x x + 1 (x + 1)

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What is x*sqrt(x^3+3x^2+3x+1) ?
The solution to x*sqrt(x^3+3x^2+3x+1) is xsqrt(x+1)(x+1)