What is expand (2+y)^5 ?

The solution to expand (2+y)^5 is 32+80y+80y^2+40y^3+10y^4+y^5

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expand (2+y)^5

expand

(2 + y)^{5}

32 + 80 y + 80 y^{2} + 40 y^{3} + 10 y^{4} + y^{5}

Solution steps

(2 + y)^{5}

Apply binomial theorem:

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

a = 2, b = y

= i = 0 \sum 5 (i 5) \cdot 2^{(5 - i)} y^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 2^{5} y^{0} : 32

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 2^{4} y^{1} : 80 y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 2^{3} y^{2} : 80 y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 2^{2} y^{3} : 40 y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 2^{1} y^{4} : 10 y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 2^{0} y^{5} : y^{5}

= 32 + 80 y + 80 y^{2} + 40 y^{3} + 10 y^{4} + y^{5}

(- 7 + 3 i) (3 + 2 i)

- 2^{- x}

(x - 2) (x + 3)

\frac{2 x ^{4} + 4 x ^{3} - x ^{2}}{x}

(4 x - 2 y)^{3}

What is expand (2+y)^5 ?
The solution to expand (2+y)^5 is 32+80y+80y^2+40y^3+10y^4+y^5