Question

1. Expand the following:
(i) (x + 2a)^5​

Answer 1

Answer:

x⁵ + 10x⁴a + 40x³a² + 80x²a³ + 80xa⁴ + 32a⁵

Step-by-step explanation:

(x + 2a)⁵

⇒ (x + 2a)[(x + 2a)²]²

⇒ (x + 2a)[x² + 4ax + 4a²]²

⇒ (x + 2a)(x⁴ + 24a²x² + 16a⁴ + 8ax³ + 32a³x)

⇒ x⁵ + 24a²x³ + 16a⁴x + 8ax⁴ + 32a³x² + 2ax⁴ + 48a³x² + 32a⁵ + 16a²x³ + 64a⁴x

⇒ x⁵ + 10x⁴a + 40x³a² + 80x²a³ + 80xa⁴ + 32a⁵

(OR)

(x + y)⁵ = x⁵ + 5x⁴y + 10x³y² + 10x²y³ + 5xy⁴ + y⁵

Substitute y = 2a

(x + 2a)⁵ = x⁵ + 10x⁴a + 40x³a² + 80x²a³ + 80xa⁴ + 32a⁵

Hoping that I have not made any mistakes, You're welcome.

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GeniusH