Respuesta :
Answer: a = 16
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Explanation:
Let's expand out that given expression.
First I'll let w = y-4x to make distribution a bit easier
[tex](y-4x)(y^2+4y+16)\\\\w(y^2+4y+16)\\\\wy^2+4wy+16w\\\\[/tex]
Now plug w = y-4x back in and distribute three more times
[tex]wy^2+4wy+16w\\\\y^2(w)+4y(w)+16(w)\\\\y^2(y-4x)+4y(y-4x)+16(y-4x)\\\\y^3-4xy^2+4y^2-\boldsymbol{16}xy+16y-64x\\\\[/tex]
Notice that the only [tex]xy[/tex] term here is the [tex]-16xy[/tex]
Comparing this to the form [tex]-axy[/tex] shows that [tex]\boldsymbol{a = 16}[/tex]
