What is expand (2^{1/2}+1)^3 ?

The solution to expand (2^{1/2}+1)^3 is 5*2^{1/2}+7

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expand (2^{1/2}+1)^3

expand

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

5 \cdot 2^{\frac{1}{2}} + 7

Decimal Notation

14.07106 \dots

Solution steps

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

Apply Perfect Cube Formula:

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

(2^{\frac{1}{2}} + 1)^{3} = (2^{\frac{1}{2}})^{3} + 3 (2^{\frac{1}{2}})^{2} \cdot 1 + 3 \cdot 2^{\frac{1}{2}} \cdot 1^{2} + 1^{3}

= (2^{\frac{1}{2}})^{3} + 3 (2^{\frac{1}{2}})^{2} \cdot 1 + 3 \cdot 2^{\frac{1}{2}} \cdot 1^{2} + 1^{3}

(2^{\frac{1}{2}})^{3} + 3 (2^{\frac{1}{2}})^{2} \cdot 1 + 3 \cdot 2^{\frac{1}{2}} \cdot 1^{2} + 1^{3} = 5 \cdot 2^{\frac{1}{2}} + 7

= 5 \cdot 2^{\frac{1}{2}} + 7

- (4 x^{4} - 4 x^{2} + 5) (10 x^{\frac{2}{3}})

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

9 y x^{2} - 24 x y + 16 y - 6 y x^{2} + 150 y

2^{2} - 4 (2) + 4

, (60 + \frac{r}{3} - (30 + r))

What is expand (2^{1/2}+1)^3 ?
The solution to expand (2^{1/2}+1)^3 is 5*2^{1/2}+7