Question

Find the value of (x+2y)³​

Answer 1

If we carefully observe it is in the form of (a+b)³ identity. Where :

• a = x
• b = 2y

So we will use the same identity and the same expansion in order to find the value of (x+2y)³ .

(a+b)³ = a³ + b³ + 3a²b + 3ab²

This expansion can also be written as

(a+b)³ = a³ + b³ + 3ab (a+b)

So substitute the values we simplify it as :

(a+b)³ = a³ + b³ + 3a²b + 3ab²

(x+2y)³ = x³ + 2y³ + 3 × x² × 2y + 3 × x × 2y²

(x+2y)³ = x³ + 8y³ + 6x²y + 12xy²

So the expansion of (x+2y)³ is x³ + 8y³ + 6x²y + 12xy² .

|| ★ || Additional Information || ★ ||

• Some more important identities have been stated below . They too just have to be put up the value to simplify.

➜ (a+b)² = a² + 2ab + b²

➜(a-b)² = a² - 2ab + b²

➜ (a+b)(a-b) = a²-b²

➜(x+a)(x+b) = x² + (a+b)x + ab

Answer 2

Given

• (x+2y)³

We Find

• Value of (x+2y)³

Identity used

• ( A + B )³

According to the question

= (a+b)³ = a³ + b³ +3a²b + 3ab²

So,

(x+2y)³ = x³ + 2y³ + 3 × 2y × x² + 3 × x × 2y²

(x+2y)³ = x³ + 8y³ + 6x²y + 12xy²

So The Expansion of (x+2y)³ is x³ + 8y³ + 6x²y + 12xy²

$\:$