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Coordinate Geometry
Question
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Simplify: (x + y)3 - (x - y)3 - 6y(x2 - y2)    

Answer

Let x + y = a, x - y = b
Then, ab = (x + y) (x - y) = x2 - y2
and    a - b = (x + y) - (x - y) = 2y
Now, (x + y)3 - (x - y)3 - 6y (x2 - y2)
= (x + y)3 - (x - y)3 - 3(2y) (x2 - y2)
= a3 - b3 - 3(a - b) ab
= (a - b)3 | Using Identity VII      
= {(x + y) - (x - y)}3
= (2y)3 = 8y3   

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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