Question

21. Factorise the expressions and then divide :
12xy(9x^2 - 16y^2) ÷ 4xy(3x + 4y)​

Answer 1

GIVEN :-

• 12xy(9x² - 16y²)/4xy(3x + 4y)

TO FIND :-

• The value of 12xy(9x² - 16y²)/4xy(3x + 4y)

SOLUTION :-

We have,

$\implies \displaystyle \sf \: \frac{12xy(9x ^{2} - 16y ^{2} )}{4xy(3x + 4y)}$

$\implies \displaystyle \sf \: \frac{12xy \bigg((3x )^{2} - (4y) ^{2} \bigg)}{4xy(3x + 4y)}$

Now by using identity :- a² - b² = (a + b)(a - b),

$\implies \displaystyle \sf \: \frac{12xy \bigg( \cancel{(3x + 4y)} (3x - 4y) \bigg)}{4xy \cancel{(3x + 4y)}}$

$\implies \displaystyle \sf \: \frac{ \cancel{12xy}(3x - 4y)}{ \cancel{4xy}}$

$\implies \displaystyle \sf \:\frac{12xy(9x ^{2} - 16y ^{2} )}{4xy(3x + 4y)} = 3(3x - 4y)$

Answer 2

Answer:

3(3x-4y)

Solution is in this attachment