q5) Factorise the expression and divide then as directed

iv)

4 yz ( z^2 + 6z -16 ) \div 2y ( z+8 )

Answers (1)

We first simplify our numerator 
So,
         4yz( z^2+ 6z - 16)
           Add and subtract 64 \Rightarrow4yz( z^2- 64 + 6z - 16 + 64)
                                            = 4yz(z^2-8^2 + 6z + 48)
                                             = 4yz((z + 8)(z - 8) + 6(z + 8))                                        using \ a^{2} -b^{2} = (a - b)(a + b)
                                             = 4yz (z + 8)(z - 8 + 6)
                                              = 4yz(z + 8)(z - 2)
Now,
                 \frac{4yz(z^{2}+6z-16)}{2y(z+8)} = \frac{4yz(z+8)(z-2)}{2y(z+8)}= 2z(z-2)

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