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Popular >

expand (3x+1)^4

Solution

expand

(3 x + 1)^{4}

Solution

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

Solution steps

(3 x + 1)^{4}

Apply binomial theorem:

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

a = 3 x, b = 1

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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