Question

15(y+3)(y^2-16)/5(y^2-y-12)

Answer 1

$\textbf {Hey there, here is the solution.}$

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

Factorise the numerator a² - b² = (a - b)(a + b)

$= \dfrac{15(y + 3)(y - 4)( y + 4)}{5(y^2 - y -12)}$

Factorise the denominator:

$= \dfrac{15(y + 3)(y - 4)( y + 4)}{5(y + 3)(y - 4)}$

Cross out common factors:

$= 5(y + 4)$

Answer: 5(y + 4)

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⭐$\textbf {Cheers}$⭐

Answer 2

Answer:

15(y+3)(y  2  −16)÷5(y  2  −y−12)

y  2  −16=(y)  2  −(4)  2

=(y+4)(y−4)

2  −y−12=y  2  −4y+3y−12

=y(y−4)+3(y−4)

=(y−4)(y+3)

Now,

5(y  2  −y−12) 15(y+3)(y  2 −16)

​ =  5(y−4)(y+3) 15×(y+3)(y+4)(y−4)

​ =3(y+4)