Question

factorise and divide:- 15(y+3)(y^2 - 16) / 5(y^2-y-12)

Answer 1

the answer after factorisation and division... (3y+4)...

Answer 2

The factorisation of $\dfrac{15(y+3)(y^{2} -16)}{5(y^{2}-y-12)}$ is $3(y+4).$

Step-by-step explanation:

We have,

$\dfrac{15(y+3)(y^{2} -16)}{5(y^{2}-y-12)}$

To find, the factorisation of $\dfrac{15(y+3)(y^{2} -16)}{5(y^{2}-y-12)}=?$

∴ $\dfrac{15(y+3)(y^{2} -16)}{5(y^{2}-y-12)}$

$=\dfrac{5(y+3)(y^{2}-4^{2} )}{(y^{2}-4y+3y-12)}$

$=\dfrac{5(y+3)(y+4)(y-4)}{(y+3)(y-4)}$

[ ∵ $a^{2} -b^{2} =(a+b)(a-b)$]

$=3(y+4)$

Hence, the factorisation of $\dfrac{15(y+3)(y^{2} -16)}{5(y^{2}-y-12)}$ is $3(y+4).$