Use the binomial expansion formula for (a+b)3.

April 1, 2026Mathematics

ScanSolve AI Answer

April 1, 2026

Answer

$1 + \frac{6}{x} + \frac{12}{x^2} + \frac{8}{x^3}$

Step 1: Use the binomial expansion formula for $(a+b)^3$ . The formula is $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$ . In this case, $a=1$ and $b=\frac{2}{x}$ .

Step 2: Substitute the values of $a$ and $b$ into the formula. $\left(1 + \frac{2}{x}\right)^3 = (1)^3 + 3(1)^2\left(\frac{2}{x}\right) + 3(1)\left(\frac{2}{x}\right)^2 + \left(\frac{2}{x}\right)^3$

Step 3: Simplify each term. $= 1 + 3(1)\left(\frac{2}{x}\right) + 3(1)\left(\frac{4}{x^2}\right) + \left(\frac{8}{x^3}\right)$ $= 1 + \frac{6}{x} + \frac{12}{x^2} + \frac{8}{x^3}$

The expanded form is: $1 + \frac{6{x} + \frac{12}{x^2} + \frac{8}{x^3}}$

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Quick Answer

Use the binomial expansion formula for (a+b)^3. The formula is (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.

Asked on April 1, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 1, 2026

Step 1: Use the binomial expansion formula for (a+b)^3. The formula is (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3. In this case, a=1 and b=(2)/(x). Step 2: Substitute the values of a and b into the formula. (1 + (2)/(x))^3 = (1)^3 + 3(1)^2((2)/(x)) + 3(1)((2)/(x))^2 + ((2)/(x))^3 Step 3: Simplify each term. = 1 + 3(1)((2)/(x)) + 3(1)((4)/(x^2)) + ((8)/(x^3)) = 1 + (6)/(x) + (12)/(x^2) + (8)/(x^3) The expanded form is: 1 + (6)/(x) + (12)/(x^2) + (8)/(x^3)