First, multiply the two terms on the left. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
#(color(red)(w) + color(red)(4))(color(blue)(w) + color(blue)(1))(w - 4)# becomes:
#((color(red)(w) xx color(blue)(w)) + (color(red)(w) xx color(blue)(1)) + (color(red)(4) xx color(blue)(w)) + (color(red)(4) xx color(blue)(1)))(w - 4)#
#(w^2 + 1w + 4w + 4)(w - 4)#
We can now combine like terms:
#(w^2 + (1 + 4)w + 4)(w - 4)#
#(w^2 + 5w + 4)(w - 4)#
We now repeat this process for the two remaining terms:
#(color(red)(w^2) + color(red)(5w) + color(red)(4))(color(blue)(w) - color(blue)(4))# becomes:
#(color(red)(w^2) xx color(blue)(w)) - (color(red)(w^2) xx color(blue)(4)) + (color(red)(5w) xx color(blue)(w)) - (color(red)(5w) xx color(blue)(4)) + (color(red)(4) xx color(blue)(w)) - (color(red)(4) xx color(blue)(4))#
#w^3 - 4w^2 + 5w^2 - 20w + 4w - 16#
We can now combine like terms:
#w^3 + (-4 + 5)w^2 + (-20 + 4)w - 16#
#w^3 + 1w^2 + (-16)w - 16#
#w^3 + w^2 - 16w - 16#
