What is expand (x^2+3x+9)^3 ?

The solution to expand (x^2+3x+9)^3 is x^6+9x^5+54x^4+189x^3+486x^2+729x+729

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expand (x^2+3x+9)^3

expand

(x^{2} + 3 x + 9)^{3}

x^{6} + 9 x^{5} + 54 x^{4} + 189 x^{3} + 486 x^{2} + 729 x + 729

Solution steps

(x^{2} + 3 x + 9)^{3}

Simplify

(x^{2} + 3 x + 9)^{3} : (x^{2} + 3 x + 9) (x^{2} + 3 x + 9) (x^{2} + 3 x + 9)

= (x^{2} + 3 x + 9) (x^{2} + 3 x + 9) (x^{2} + 3 x + 9)

Expand

(x^{2} + 3 x + 9) (x^{2} + 3 x + 9) : x^{4} + 6 x^{3} + 27 x^{2} + 54 x + 81

= (x^{4} + 6 x^{3} + 27 x^{2} + 54 x + 81) (x^{2} + 3 x + 9)

Distribute parentheses

= x^{4} x^{2} + x^{4} \cdot 3 x + x^{4} \cdot 9 + 6 x^{3} x^{2} + 6 x^{3} \cdot 3 x + 6 x^{3} \cdot 9 + 27 x^{2} x^{2} + 27 x^{2} \cdot 3 x + 27 x^{2} \cdot 9 + 54 x x^{2} + 54 x \cdot 3 x + 54 x \cdot 9 + 81 x^{2} + 81 \cdot 3 x + 81 \cdot 9

Simplify

x^{4} x^{2} + x^{4} \cdot 3 x + x^{4} \cdot 9 + 6 x^{3} x^{2} + 6 x^{3} \cdot 3 x + 6 x^{3} \cdot 9 + 27 x^{2} x^{2} + 27 x^{2} \cdot 3 x + 27 x^{2} \cdot 9 + 54 x x^{2} + 54 x \cdot 3 x + 54 x \cdot 9 + 81 x^{2} + 81 \cdot 3 x + 81 \cdot 9 : x^{6} + 9 x^{5} + 54 x^{4} + 189 x^{3} + 486 x^{2} + 729 x + 729

= x^{6} + 9 x^{5} + 54 x^{4} + 189 x^{3} + 486 x^{2} + 729 x + 729

f (x) \cdot x^{2} + 5 x - 6

x^{2} - 2 x - y^{2} + 2 y

\frac{1 ^{4} ( x ^{2} ) ^{2} + 3 ^{3} - 2 ^{5}}{4}

36 x^{2} - 24 x \cdot y^{2} + 4 y^{4}

- 18 a - 27 c

What is expand (x^2+3x+9)^3 ?
The solution to expand (x^2+3x+9)^3 is x^6+9x^5+54x^4+189x^3+486x^2+729x+729