Question

Factorise the following expressions :—

( 2m + 3n )² - ( 3m + 2n )²​

Answer 1

Answer:

-5(m + n)(m - n)

Step-by-step explanation:

(2m + 3n)² - (3m + 2n )²= (2m + 3n + 3m + 2n) [ 2m + 3n - (3m + 2n)]= (5m + 5n)(-m + n)=

-5(m + n)(m - n)

Answer 2

Factorise:

$:\implies\sf (2m + 3n)^2 - (3m + 2n)^2$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf (2m)^2 + (3n)^2 + 2 \times 2m \times 3n - (3m)^2 + (2n)^2 + 2 \times 3m \times 2n$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 4m^2 + 9n^2 + 12mn - (9m^2 + 4n^2 + 12mn)$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 4m^2 + 9n^2 + 12mn - 9m^2 - 4n^2 - 12mn$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 4m^2 + 9n^2 + \cancel{12mn} - 9m^2 - 4n^2 - \cancel{12mn}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 4m^2 + 9n^2 - 9m^2 - 4n^2$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf -5m^2 + 5n^2$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 5(n^2 - m^2)$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 5(n + m)(n - m)\;\;\;\;\;\;\;\;\bigg\lgroup\bf (a^2 - b^2) = (a + b)(a - b)\bigg\rgroup$

⠀⠀⠀⠀⠀⠀⠀

$:\implies{\underline{\boxed{\sf{\purple{5(n + m)(n - m)\;or\; -5(m + n)(m - n)}}}}}\;\bigstar$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\boxed{\underline{\underline{\bigstar \: \bf\:Factoring\:formulas\:\bigstar}}}$

For any real number a and b,

⠀⠀⠀⠀⠀⠀⠀

• $\sf (a + b)^2 = a^2 + 2ab + b^2$

• $\sf (a - b)^2 = a^2 - 2ab + b^2$

• $\sf a^2 - b^2 = (a + b)(a - b)$

• $\sf a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

• $\sf a^3 + b^3 = (a + b)(a^2 - ab + b^2)$