What is expand (5a+y)^5 ?

The solution to expand (5a+y)^5 is 3125a^5+3125a^4y+1250a^3y^2+250a^2y^3+25ay^4+y^5

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expand (5a+y)^5

expand

(5 a + y)^{5}

3125 a^{5} + 3125 a^{4} y + 1250 a^{3} y^{2} + 250 a^{2} y^{3} + 25 a y^{4} + y^{5}

Solution steps

(5 a + y)^{5}

Apply binomial theorem:

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

a = 5 a, b = y

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

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (5 a)^{5} y^{0} : 3125 a^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (5 a)^{4} y^{1} : 3125 a^{4} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (5 a)^{3} y^{2} : 1250 a^{3} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (5 a)^{2} y^{3} : 250 a^{2} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (5 a)^{1} y^{4} : 25 a y^{4}

Simplify

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

= 3125 a^{5} + 3125 a^{4} y + 1250 a^{3} y^{2} + 250 a^{2} y^{3} + 25 a y^{4} + y^{5}

(x + 3) (x^{2} + 3 x + 9)

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

- 2 (x + 1)^{2} + (x + 1) - 1

\frac{\frac{3}{4} \cdot 120}{1}

64 u^{3} - z^{3}

What is expand (5a+y)^5 ?
The solution to expand (5a+y)^5 is 3125a^5+3125a^4y+1250a^3y^2+250a^2y^3+25ay^4+y^5