What is expand (3x+8)^5 ?

The solution to expand (3x+8)^5 is 243x^5+3240x^4+17280x^3+46080x^2+61440x+32768

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expand (3x+8)^5

expand

(3 x + 8)^{5}

243 x^{5} + 3240 x^{4} + 17280 x^{3} + 46080 x^{2} + 61440 x + 32768

Solution steps

(3 x + 8)^{5}

Apply binomial theorem:

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

a = 3 x, b = 8

= i = 0 \sum 5 (i 5) (3 x)^{(5 - i)} \cdot 8^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} (3 x)^{5} \cdot 8^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (3 x)^{4} \cdot 8^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (3 x)^{3} \cdot 8^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (3 x)^{2} \cdot 8^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (3 x)^{1} \cdot 8^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (3 x)^{0} \cdot 8^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 x)^{5} \cdot 8^{0} : 243 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (3 x)^{4} \cdot 8^{1} : 3240 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 x)^{3} \cdot 8^{2} : 17280 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 x)^{2} \cdot 8^{3} : 46080 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (3 x)^{1} \cdot 8^{4} : 61440 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (3 x)^{0} \cdot 8^{5} : 32768

= 243 x^{5} + 3240 x^{4} + 17280 x^{3} + 46080 x^{2} + 61440 x + 32768

(a + b - c)^{2} + (a - b - c)^{2} - 2 (b - c)

36 j^{2} - 100 k

(3 q + b)^{3}

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

6 x^{2} y - 4 x^{2} + 12 x y^{2} - 8 x y

What is expand (3x+8)^5 ?
The solution to expand (3x+8)^5 is 243x^5+3240x^4+17280x^3+46080x^2+61440x+32768