x+y) in expanded form can be written as:
Oz (X+Y)(x2 - XY-Y)
Ves (X+Y)(x² + XY + y2)
(b) (X+Y)(x2 - XY+Y2
(x - Y)(x2 + XY+Y2)
(d)
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9th
Maths
Polynomials
Algebraic Identities
Verify x^3 - y^3 = (x - y)(...
MATHS
Verify x
3
−y
3
=(x−y)(x
2
+xy+y
2
) using some non-zero positive integers and check by actual multiplication. Can you call theses as identities?
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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.
Yes, we can call it as an identity: For example:
Let us take x=2 and y=1 in x
3
−y
3
=(x−y)(x
2
+xy+y
2
) then the LHS and RHS will be equal as shown below:
2
3
−1
3
=7 and
(2−1)(2
2
+(2×1)+1
2
)=1(5+2)=1×7=7
Therefore, LHS=RHS
Hence, x
3
−y
3
=(x−y)(x
2
+xy+y
2
) can be used as an identity