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

The solution to expand (5x+3)^5 is 3125x^5+9375x^4+11250x^3+6750x^2+2025x+243

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expand (5x+3)^5

expand

(5 x + 3)^{5}

3125 x^{5} + 9375 x^{4} + 11250 x^{3} + 6750 x^{2} + 2025 x + 243

Solution steps

(5 x + 3)^{5}

Apply binomial theorem:

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

a = 5 x, b = 3

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

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (5 x)^{5} \cdot 3^{0} : 3125 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (5 x)^{4} \cdot 3^{1} : 9375 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (5 x)^{3} \cdot 3^{2} : 11250 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (5 x)^{2} \cdot 3^{3} : 6750 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (5 x)^{1} \cdot 3^{4} : 2025 x

Simplify

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

= 3125 x^{5} + 9375 x^{4} + 11250 x^{3} + 6750 x^{2} + 2025 x + 243

- 0.98 (9.8)

\frac{13}{20}

\frac{1}{x ^{- \frac{1}{2}}}

\frac{2}{3} - 8

(- a^{m}) (- 2 ab) (- 3 a^{2} b^{x})

What is expand (5x+3)^5 ?
The solution to expand (5x+3)^5 is 3125x^5+9375x^4+11250x^3+6750x^2+2025x+243