What is expand (x^2-3y)^4 ?

The solution to expand (x^2-3y)^4 is x^8-12x^6y+54x^4y^2-108x^2y^3+81y^4

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expand (x^2-3y)^4

expand

(x^{2} - 3 y)^{4}

x^{8} - 12 x^{6} y + 54 x^{4} y^{2} - 108 x^{2} y^{3} + 81 y^{4}

Solution steps

(x^{2} - 3 y)^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x^{2}, b = - 3 y

= i = 0 \sum 4 (i 4) (x^{2})^{(4 - i)} (- 3 y)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} (- 3 y)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} (- 3 y)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (x^{2})^{2} (- 3 y)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} (- 3 y)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} (- 3 y)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} (- 3 y)^{0} : x^{8}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} (- 3 y)^{1} : - 12 x^{6} y

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x^{2})^{2} (- 3 y)^{2} : 54 x^{4} y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} (- 3 y)^{3} : - 108 x^{2} y^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} (- 3 y)^{4} : 81 y^{4}

= x^{8} - 12 x^{6} y + 54 x^{4} y^{2} - 108 x^{2} y^{3} + 81 y^{4}

5 x^{4} - 10 x^{2} - 315

\frac{2}{5} \times \frac{3}{2}

- 16 x - 9

(s + 1)^{3} (s + 3)

lo g_{2} (8^{4})

What is expand (x^2-3y)^4 ?
The solution to expand (x^2-3y)^4 is x^8-12x^6y+54x^4y^2-108x^2y^3+81y^4