What is expand (5+2y)^4 ?

The solution to expand (5+2y)^4 is 625+1000y+600y^2+160y^3+16y^4

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expand (5+2y)^4

expand

(5 + 2 y)^{4}

625 + 1000 y + 600 y^{2} + 160 y^{3} + 16 y^{4}

Solution steps

(5 + 2 y)^{4}

Apply binomial theorem:

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

a = 5, b = 2 y

= i = 0 \sum 4 (i 4) \cdot 5^{(4 - i)} (2 y)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 5^{4} (2 y)^{0} : 625

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 5^{3} (2 y)^{1} : 1000 y

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 5^{2} (2 y)^{2} : 600 y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 5^{1} (2 y)^{3} : 160 y^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 5^{0} (2 y)^{4} : 16 y^{4}

= 625 + 1000 y + 600 y^{2} + 160 y^{3} + 16 y^{4}

\frac{1 + 3 i}{2 i}

1 + \frac{1}{1 + x}

9 + 42

\frac{5 - 10 i}{9 + 6 i}

\frac{7}{8} o f^{1000}

What is expand (5+2y)^4 ?
The solution to expand (5+2y)^4 is 625+1000y+600y^2+160y^3+16y^4