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Q.

Is it true that $x 3 + y 3 = (x + y) x 2 − x y + y 2$ ?

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a

True

b

False

answer is A.

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Detailed Solution

The given expression is

x 3 + y 3 = x + y x 2 − x y + y 2

.
We have to find the validity of the polynomial.
We can multiply the terms containing the variables on the right–hand side of this identity and obtain the expanded form and then simplify to get the respective value on the left–hand side of the identity.
Now, we have the following observation.
The right–hand side of the polynomial is expanded in the following way to get the simplification.

= x + y x 2 − x y + y 2 = x (x 2 − x y + y 2) + y (x 2 − x y + y 2) = x 3 − x 2 y + x y 2 + x 2 y − x y 2 + y 3 = x 3 + (x 2 y − x 2 y) + (x y 2 − x y 2) + y 3 = x 3 + y 3

Hence, it is verified that

x 3 + y 3 = x + y x 2 − x y + y 2

.
Hence, the given statement

x 3 + y 3 = (x + y) x 2 − x y + y 2

is true.
Therefore, the correct option is 1.

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Is it true that x 3 + y 3 =(x+y) x 2 −xy+ y 2 ?