Question

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

Answer 1

$<b>Heya mate. (^_-). Solution below.$
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$<u>Question -</u>$

Simplify :

[(3a - 2b)(9a² + 6ab + 4b²)] - [(2a +3b)(4a² - 6ab + 9b²)]
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$<u>Solution -</u>$

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

We divide the equation in three parts for convenience.
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$\mathcal{\underline{First \: part}}$

[(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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$\mathcal{\underline{Second \: part}}$

[(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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$\mathcal{\underline{Third\: part}}$

• [(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 .....$\mathcal{\red{\boxed{Answer!!!}}}$


$<marquee>Hence, the answer is 19a³ - 35b³.</marquee>$
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Thank you... ;-)

Answer 2

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