What is the product of -3x²y and 5xy²-xy?
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Answer:
The product is (x-y)(x+y)(x^2+y^2)=x^4-y^4(x−y)(x+y)(x
2
+y
2
)=x
4
−y
4
Step-by-step explanation:
To find : The product of (x-y),(x+y)\text{ and }(x^2+y^2)(x−y),(x+y) and (x
2
+y
2
)
Solution :
Write the expression as,
(x-y)(x+y)(x^2+y^2)(x−y)(x+y)(x
2
+y
2
)
Applying identity, (x-y)(x+y)=x^2-y^2(x−y)(x+y)=x
2
−y
2
=(x^2-y^2)(x^2+y^2)=(x
2
−y
2
)(x
2
+y
2
)
Again apply the same identity with x=x^2,y=y^2x=x
2
,y=y
2
=(x^2)^2-(y^2)^2=(x
2
)
2
−(y
2
)
2
=x^4-y^4=x
4
−y
4
Therefore, (x-y)(x+y)(x^2+y^2)=x^4-y^4(x−y)(x+y)(x
2
+y
2
)=x
4
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