Question

Expand the expression \((1- 2x)^ 5\).

Answer 1

Given:

(1 − 2x)⁵

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Step 1: Use Binomial Theorem

(a − b)⁵ = a⁵ − 5a⁴b + 10a³b² − 10a²b³ + 5ab⁴ − b⁵

Let
a = 1,   b = 2x

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Step 2: Substitute and simplify each term

a⁵ = 1

5a⁴b = 5(2x) = 10x

10a³b² = 10(2x)² = 40x²

10a²b³ = 10(2x)³ = 80x³

5ab⁴ = 5(2x)⁴ = 80x⁴

b⁵ = (2x)⁵ = 32x⁵

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Step 3: Write the expansion

(1 − 2x)⁵ =

1 − 10x + 40x² − 80x³ + 80x⁴ − 32x⁵

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Final Answer:

(1 − 2x)⁵ = 1 − 10x + 40x² − 80x³ + 80x⁴ − 32x⁵