Question

factorise (3a+b)² - (a-2b)²​

Answer 1

Given  : (3a+b)² - (a-2b)²​

To Find : Factorize

Solution:

(3a+b)² - (a-2b)²​

x² - y² = (x + y)(x - y)

x = (3a + b)

y = ( a - 2b)

(3a+b)² - (a-2b)²​

= ( (3a + b) + (a - 2b) ) ( (3a + b) - (a - 2b) )

= (3a + b + a - 2b)(3a + b - a + 2b)

= (3a + a + b - 2b)(3a - a + b + 2b)

= ( 4a - b)(2a + 3b)

(3a+b)² - (a-2b)²​ = ( 4a - b)(2a + 3b)

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Answer 2

Answer :-

• $\rm \bf(3a + b) ^{2} - (a - 2b) ^{2} = (4a - b)(2a + 3b)$

Question :-

$\rm \: Factorise (3a + b)^{2} - {(a - 2b)}^{2}$

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Formula :-

$\rm \: {a}^{2} - {b}^{2} = (a + b)(a - b)$

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Let :-

• Let A be ( 3a + b )
• Let B be ( a - 2b )

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Solution :-

$\rm \:(3a + b)^{2} - {(a - 2b)}^{2}$

Applying the formula ,

$\rm \implies[(3a + b) + (a - 2b)] \: \: [(3a + b) - (a - 2b)]$

opening the brackets ,

$\rm \implies(3a + b+ a - 2b) \: \: (3a + b - a + 2b)]$

Making the variables to their same side,

$\rm \implies(3a + a+ b - 2b) \: \: (3a - a + b + 2b)]$

$\rm \implies \bf \: (4a -b)(2a + 3b)$

$\sf \therefore \bf(3a + b) ^{2} - (a - 2b) ^{2} = (4a - b)(2a + 3b)$

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