Question

(y² + 5y) (y² + 5y $-$ 2) $-$ 24

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}\left(y^2+5y\right)\left(y^2+5y-2\right)-24. \\ \mathrm{Let}{y}^2+5y=a \\ \therefore \left(y^2+5y\right)\left(y^2+5y-2\right)-24=a\left(a-2\right)-24 \\ =a^2-2a-24 \\ =a^2-6a+4a-24 \\ =a\left(a-6\right)+4\left(a-6\right) \\ =\left(a-6\right)\left(a+4\right) \\ \mathrm{Resubstituting}\mathrm{the}\mathrm{value}\mathrm{of}a,\mathrm{we}\mathrm{get}: \\ \left(y^2+5y\right)\left(y^2+5y-2\right)-24=\left(y^2+5y-6\right)\left(y^2+5y+4\right) \\ =\left(y^2+6y-y-6\right)\left(y^2+4y+y+4\right) \\ =\left[y\left(y+6\right)-1\left(y+6\right)\right]\left[y\left(y+4\right)+1\left(y+4\right)\right] \\ =\left(y+6\right)\left(y-1\right)\left(y+4\right)\left(y+1\right) \end{gathered}$$