Question

find the binomial (x^2-a^2)(x-a)
​

Answer 1

Suppose (a−b) and (c−d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.
(a−b)×(c−d)=a×(c−d)−b×(c−d)=(a×c−a×d)−(b×c−b×d)
=ac−ad−bc+bd
Let,
a=x
2
,b=a
2
,c=x,d=a
Now,
=x
2
×(x−a)−a
2
×(x−a)
=[(x
2
×x)+((a
2
×x)+(a
2
×−a)]
=[x
3
−x
2
a−a
2
x+a
3
]