Question

(3a − 2b)x(9a2 +4b2 +6ab)​

Answer 1

Step-by-step explanation:

Simplify :

[(3a - 2b)(9a² + 6ab + 4b²)] - [(2a +3b)(4a² - 6ab + 9b²)]

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[(3a - 2b)(9a² + 6ab + 4b²)] - [(2a +3b)(4a² - 6ab + 9b²)]

We divide the equation in three parts for convenience.

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[(3a - 2b)(9a² + 6ab + 4b²)]

We can write it as -

[(3a - 2b){(3a)² + (3a × 2b) + (2b)²}]

• Now, using the identity -

(a - b)(a² + ab + b²) = a³ - b³

So let -

3a = a

2b = b

Then,

[(3a - 2b){(3a)² + (3a × 2b) + (2b)²}]

= [(3a)³ - (2b)³]

= (27a³ - 8b³)....... Equation (i)

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[(2a + 3b)(4a² - 6ab + 9b²)]

We can write it as -

[(2a + 3b){(2a)² - (2a × 3b) + (3b)²}]

• Now, using the formula -

(a + b)(a² - ab + b²) = a³ + b³

So let -

2a = a

3b = b

Then,

[(2a + 3b){(2a)² - (2a × 3b) + (3b)²}]

= [(2a)³ + (3b)³]

= (8a³ + 27b³)...... Equation (ii)

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• [(3a - 2b)(9a² + 6ab + 4b²)] - [(2a +3b)(4a² - 6ab + 9b²)]

• = [(27a³ - 8b³) - (8a³ + 27b³)]..... [from equations (i) and (ii)

• = [27a³ - 8b³ - 8a³ - 27b³].....[removing the brackets]

• = [27a³ - 8a³ - 8b³ - 27b³]......[rearranging the terms]

• = 19a³ - 35b³ .....

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