q5) Factorise the expression and divide then as directed  

vi) 

12 xy ( 9 x^2 - 16 y^2 ) \div 4 xy ( 3 x + 4 y )

Answers (1)

We first simplify our numerator,
                                   12xy(9x^{2} -16y^{2}) = 12xy(3x)^{2} -(4y)^{2}                                                                                                                      using (a)^{2} -(b)^{2} = (a-b)(a+b)
                                                                    = 12xy((3x - 4y)(3x + 4y))
Now,
               \frac{12xy(9x^{2} - 16y^{2})}{4xy(3x + 4y)} = \frac{12xy(3x+4y)(3x-4y)}{4xy(3x+4y)} = 3(3x-4y) 

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