What is expand (2x+1)^3*e^{5x} ?

The solution to expand (2x+1)^3*e^{5x} is 8e^{5x}x^3+12e^{5x}x^2+6e^{5x}x+e^{5x}

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expand (2x+1)^3*e^{5x}

expand

(2 x + 1)^{3} \cdot e^{5 x}

8 e^{5 x} x^{3} + 12 e^{5 x} x^{2} + 6 e^{5 x} x + e^{5 x}

Solution steps

(2 x + 1)^{3} e^{5 x}

(2 x + 1)^{3} = 8 x^{3} + 12 x^{2} + 6 x + 1

= e^{5 x} (8 x^{3} + 12 x^{2} + 6 x + 1)

= e^{5 x} (8 x^{3} + 12 x^{2} + 6 x + 1)

Distribute parentheses

= e^{5 x} \cdot 8 x^{3} + e^{5 x} \cdot 12 x^{2} + e^{5 x} \cdot 6 x + e^{5 x} \cdot 1

= 8 e^{5 x} x^{3} + 12 e^{5 x} x^{2} + 6 e^{5 x} x + 1 \cdot e^{5 x}

Multiply:

1 \cdot e^{5 x} = e^{5 x}

= 8 e^{5 x} x^{3} + 12 e^{5 x} x^{2} + 6 e^{5 x} x + e^{5 x}

(2 cos (x) + 1) (2 cos (3 x) - 2)

(1 + \frac{s}{100}) (1 + \frac{s}{1000}) (1 + \frac{s}{10000})

(0.06) \cdot ((458 \cdot 5, 8) + (740 \cdot 7, 3))

\frac{3 ( 2 - t ) t}{4}

L {sin (6 t)} (s - 2)

What is expand (2x+1)^3*e^{5x} ?
The solution to expand (2x+1)^3*e^{5x} is 8e^{5x}x^3+12e^{5x}x^2+6e^{5x}x+e^{5x}