Verify: (i)x+ y2 = (x + y) (x2 - xy + y2)
(
Factorise each of the following.
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ANSWER
To prove: x
3
−y
3
=(x−y)(x
2
+xy+y
2
)
Consider the right hand side (RHS) and expand it as follows:
(x−y)(x
2
+xy+y
2
)=x
3
+x
2
y+xy
2
−yx
2
−xy
2
−y
3
=(x
3
−y
3
)+(x
2
y+xy
2
+x
2
y−xy
2
)=x
3
−y
3
=LHS
Hence proved.
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