Find the first four terms of the expansion of (1-2x)4.

March 29, 2026Mathematics

ScanSolve AI Answer

March 29, 2026

Answer

0 $or$ x=-\frac{1}{4}$.

9. The sum of the first four terms in the expansion of $(1-2x)^4$ is equal to the sum of the first three terms in the expansion of $(1-x)^8$ . Show that this is true only if $x=0$ or $x=-\frac{1}{4}$ .

Step 1: Find the first four terms of the expansion of $(1-2x)^4$ . Using the binomial theorem $(a+b)^n = \binom{n}{0}a^n + \binom{n}{1}a^{n-1}b + \binom{n}{2}a^{n-2}b^2 + \binom{n}{3}a^{n-3}b^3 + \dots$

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9. The sum of the first four terms in the expansion of (1-2x)^4 is equal to the sum of the first three terms in the expansion of (1-x)^8.

Asked on March 29, 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 March 29, 2026

9. The sum of the first four terms in the expansion of (1-2x)^4 is equal to the sum of the first three terms in the expansion of (1-x)^8. Show that this is true only if x=0 or x=-(1)/(4). Step 1: Find the first four terms of the expansion of (1-2x)^4. Using the binomial theorem (a+b)^n = n0a^n + n1a^n-1b + n2a^n-2b^2 + n3a^n-3b^3 +