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Popular >

expand (3+x)^4

Solution

expand

(3 + x)^{4}

Solution

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

Solution steps

(3 + x)^{4}

Apply binomial theorem:

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

a = 3, b = x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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