What is expand (5+3e^{7t})^4 ?

The solution to expand (5+3e^{7t})^4 is 625+1500e^{7t}+1350e^{14t}+540e^{21t}+81e^{28t}

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expand (5+3e^{7t})^4

expand

(5 + 3 e^{7 t})^{4}

625 + 1500 e^{7 t} + 1350 e^{14 t} + 540 e^{21 t} + 81 e^{28 t}

Solution steps

(5 + 3 e^{7 t})^{4}

Apply binomial theorem:

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

a = 5, b = 3 e^{7 t}

= i = 0 \sum 4 (i 4) \cdot 5^{(4 - i)} (3 e^{7 t})^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 5^{4} (3 e^{7 t})^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 5^{3} (3 e^{7 t})^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 5^{2} (3 e^{7 t})^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 5^{1} (3 e^{7 t})^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 5^{0} (3 e^{7 t})^{4}

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 5^{4} (3 e^{7 t})^{0} = 625

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 5^{3} (3 e^{7 t})^{1} : 1500 e^{7 t}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 5^{2} (3 e^{7 t})^{2} : 1350 e^{14 t}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 5^{1} (3 e^{7 t})^{3} : 540 e^{21 t}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 5^{0} (3 e^{7 t})^{4} : 81 e^{28 t}

= 625 + 1500 e^{7 t} + 1350 e^{14 t} + 540 e^{21 t} + 81 e^{28 t}

(1 + p - 2) (1 + p + 2)

(y = 2, x + 6) (\frac{x}{2} - y = 3)

- 3 (7 - 14)

- \frac{3 ( 199 + 77 73 )}{8} + 1715 + 25073

(\frac{v}{2} - 1) \cdot (y + vu)

What is expand (5+3e^{7t})^4 ?
The solution to expand (5+3e^{7t})^4 is 625+1500e^{7t}+1350e^{14t}+540e^{21t}+81e^{28t}