What is expand (3+sqrt(9-k))^3 ?

The solution to expand (3+sqrt(9-k))^3 is 36sqrt(9-k)-9k-ksqrt(9-k)+108

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expand (3+sqrt(9-k))^3

expand

(3 + 9 - k)^{3}

36 9 - k - 9 k - k 9 - k + 108

Solution steps

(3 + 9 - k)^{3}

Apply Perfect Cube Formula:

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

(3 + 9 - k)^{3} = 3^{3} + 3 \cdot 3^{2} 9 - k + 3 \cdot 3 (9 - k)^{2} + (9 - k)^{3}

= 3^{3} + 3 \cdot 3^{2} 9 - k + 3 \cdot 3 (9 - k)^{2} + (9 - k)^{3}

Simplify

3^{3} + 3 \cdot 3^{2} 9 - k + 3 \cdot 3 (9 - k)^{2} + (9 - k)^{3} : 36 9 - k - 9 k - k 9 - k + 108

= 36 9 - k - 9 k - k 9 - k + 108

(\frac{x}{y} - \frac{y}{z})^{2}

(1 - i)^{13}

\frac{6 ( 7 ^{20} - 5 ^{20} )}{7 ^{20}} - \frac{144}{49}

(5 sin (t) + sin (5 t)) (- 5 sin (t) - 5 sin (5 t))

\frac{a c ( 16 a c - 8 b ^{2} ) + b ^{4}}{4 a ^{2}}

What is expand (3+sqrt(9-k))^3 ?
The solution to expand (3+sqrt(9-k))^3 is 36sqrt(9-k)-9k-ksqrt(9-k)+108