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

The solution to expand (3y-3)^4 is 81y^4-324y^3+486y^2-324y+81

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expand (3y-3)^4

expand

(3 y - 3)^{4}

81 y^{4} - 324 y^{3} + 486 y^{2} - 324 y + 81

Solution steps

(3 y - 3)^{4}

Apply binomial theorem:

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

a = 3 y, b = - 3

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 y)^{3} (- 3)^{1} : - 324 y^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 y)^{2} (- 3)^{2} : 486 y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (3 y)^{1} (- 3)^{3} : - 324 y

Simplify

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

= 81 y^{4} - 324 y^{3} + 486 y^{2} - 324 y + 81

6 x^{2} + 5 x

- 2 \cdot (- 7)

11.4 5^{2}

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

x^{2} + (x + 1)^{2} + (x + 2)^{2}

What is expand (3y-3)^4 ?
The solution to expand (3y-3)^4 is 81y^4-324y^3+486y^2-324y+81