What is expand (3+z)^5 ?

The solution to expand (3+z)^5 is 243+405z+270z^2+90z^3+15z^4+z^5

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expand (3+z)^5

expand

(3 + z)^{5}

243 + 405 z + 270 z^{2} + 90 z^{3} + 15 z^{4} + z^{5}

Solution steps

(3 + z)^{5}

Apply binomial theorem:

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

a = 3, b = z

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

Expand summation

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

Simplify

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

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 3^{4} z^{1} : 405 z

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 3^{3} z^{2} : 270 z^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 3^{2} z^{3} : 90 z^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 3^{1} z^{4} : 15 z^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 3^{0} z^{5} : z^{5}

= 243 + 405 z + 270 z^{2} + 90 z^{3} + 15 z^{4} + z^{5}

(6 - 8 i) 2

(x + 2 y)^{2} - (3 x - y)^{2}

w^{2} + 8 w + 12

3 \frac{3}{4} \div 2

What is expand (3+z)^5 ?
The solution to expand (3+z)^5 is 243+405z+270z^2+90z^3+15z^4+z^5