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Coordinate Geometry
Question
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Verify:  x3 + y3 = (x + y)(x2 - xy + y2)

Answer

We know that
(x + y)3 = x3 + y3 + 3xy(x + y)
| Using Identity VI
⇒ x3 + y3 = (x + y)3 - 3xy(x + y)
⇒ x3 + y3 = (x + y){(x + y)2 - 3xy)
⇒ x3 + y3 = (x + y)(x2 + 2xy + y2 - 3xy)
| Using Identity I
⇒ x3 + y3 = (x + y)(x2 - xy + y2)

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Some More Questions From Coordinate Geometry Chapter

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

4x2 - 3x + 7

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

x10+ y3 + t50

Write the coefficients of x2 in each of the following:

2 + x2 + x

Write the coefficients of x2 in each of the following:
2 - x2 + x3