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Popular >

expand (3y-1)^4

Solution

expand

(3 y - 1)^{4}

Solution

81 y^{4} - 108 y^{3} + 54 y^{2} - 12 y + 1

Solution steps

(3 y - 1)^{4}

Apply binomial theorem:

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

a = 3 y, b = - 1

= i = 0 \sum 4 (i 4) (3 y)^{(4 - i)} (- 1)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (3 y)^{4} (- 1)^{0} : 81 y^{4}

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 y)^{2} (- 1)^{2} : 54 y^{2}

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (3 y)^{0} (- 1)^{4} : 1

= 81 y^{4} - 108 y^{3} + 54 y^{2} - 12 y + 1

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Frequently Asked Questions (FAQ)

What is expand (3y-1)^4 ?
The solution to expand (3y-1)^4 is 81y^4-108y^3+54y^2-12y+1