Question

Factorise (3m square -27n square) and divide (m+3n)

Answer 1

Given question : factorise ( 3m^2 - 27n^2 ) and divide by ( m + 2n )

    Solution : -

According to the question,

1 : Factorizing ( 3m^2 - 27n^2 )

⇒ 3m^ 2 - 27 n^2

⇒ 3( m^2 - 9n^2 )

⇒ 3[ m^2 - ( 3 n )^2 ]

From factorization, we know that a^2 - b^2 in factorized form is ( a + b )( a - b ).

∴ 3( m + 3n ) ( m - 3n )

Now, 3m^2 - 27n^2 has been factorized.

Therefore, dividing 3( m + 3n )( m - 3n ) by ( m + 3n ).

⇒ [ 3( m + 3n )( m - 3n ) ] / ( m + 3n )

⇒ 3( m - 3n )

Therefore, result is 3( m - 3n ).

Answer 2

$\huge\mathfrak{Solution :}$

Given Equation :-

(3m² - 27n²)

Taking 3 as common , we get

= 3(m² - 9n²)

Now, On simplifying further, we get

= 3[(m)² - (3n)²]

Using identity :-

a² - b² = (a + b)(a - b)

Here, a = m and b = 3n

Putting identity, we get

= 3[(m + 3n)(m - 3n)]

Now further question says to divide it by (m + 3n)

•°•

= 3(m + 3n)(m - 3n) / (m + 3n)

We get

= 3(m - 3n)

$\mathsf\green{= \ 3m - 9n}$

$\huge\mathbb{Hope \ this \ helps.}$