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

The solution to expand (2y^{1/2}-1)^3 is 8y^{3/2}-12y+6y^{1/2}-1

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expand (2y^{1/2}-1)^3

expand

(2 y^{\frac{1}{2}} - 1)^{3}

8 y^{\frac{3}{2}} - 12 y + 6 y^{\frac{1}{2}} - 1

Solution steps

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

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

(2 y^{\frac{1}{2}})^{3} = 8 y^{\frac{3}{2}}

3 (2 y^{\frac{1}{2}})^{2} \cdot 1 = 12 y

3 \cdot 2 y^{\frac{1}{2}} \cdot 1^{2} = 6 y^{\frac{1}{2}}

1^{3} = 1

= 8 y^{\frac{3}{2}} - 12 y + 6 y^{\frac{1}{2}} - 1

(x - y) (x - y)

\frac{5 x + 10}{( x - 5 ) ( x + 5 )}

6 \cdot (2^{\frac{1}{6}} - 1)

(cos (D) + A sin (D)) (cos (C) + A sin (C))

What is expand (2y^{1/2}-1)^3 ?
The solution to expand (2y^{1/2}-1)^3 is 8y^{3/2}-12y+6y^{1/2}-1