Question

Expand (2a-3b)^3 using suitable identity

Answer 1

We need to expand (2a−3b)3

We know suitable identity is (x−y)3=x3−3x2y+3xy2+y3

Here x=2a and y=3b

Therefore, value of (2a−3b)3 is

=(2a)3−3(2a)2(3b)+3(2a)(3b)2−(3b)3

=8a3−36a2b+54ab2−27b3

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Answer 2

Answer :-

• the expanded form is 4a² - 9b² - 36a²b + 54ab².

Given :-

• (2a - 3b)³

To Find :-

• Expanded form of this.

Solution :-

Here

• (2a - 3b)³

Identity used

• (a - b)³ = a³ - b³ - 3ab (a - b)

Let

• a = 2a
• b = 3b

According to question :-

⇒ (a - b)³ = (2a)² - (3b)² - 3.2a.3b (2a - 3b)

⇒ (a - b)³ = 4a² - 9b² - 18ab (2a - 3b)

⇒ (a - b)³ = 4a² - 9b² - 36a²b + 54ab²

Hence, the expanded form is 4a² - 9b² - 36a²b + 54ab².