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Verify that (p-q) ( p ^(2) + pq + q ^(...

Verify that
`(p-q) ( p ^(2) + pq + q ^(2)) = p ^(3) - q ^(3)`

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NCERT EXEMPLAR-ALGEBRAIC EXPRESSIONS, IDENTITIES AND FACTORISATION -EXERCISE
  1. Verify that (ab+ bc) (ab- bc) + (bc+ ca) (bc- ca) + (ca + ab) (ca- a...

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  2. Verify that (a +b + c) (a ^(2) + b ^(2) + c ^(2) - ab - bc - ca) = a...

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  3. Verify that (p-q) ( p ^(2) + pq + q ^(2)) = p ^(3) - q ^(3)

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  4. Verify that (m + n) ( m ^(2) - mn + n ^(2)) = m ^(3) + n ^(3)

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  5. Verify the (a+b ) (a+b) (a +b) = a ^(3) + 3a ^(2) b + 3a^(2) b + 3a ...

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  6. Verify that (a-b) (a -b) (a-b) = a ^(3) - 3a ^(2) b + 3a b ^(2) - b ...

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  7. Verify that (a ^(2) - b ^(2)) (a ^(2) + b ^(2)) + (b ^(2) - c ^(2)) ...

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  8. Verify that (5x + 8) ^(2) - 160 x = (5x - 8) ^(2)

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  9. Verify the (7p - 13q ) ^(2) + 364 pq = (7p + 13q) ^(2)

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  10. Verify that ((3p )/( 7) + (7)/(6p )) ^(2) - ((3p)/(7) -(7)/( 6p ))^2...

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  11. Find the value of a, if 8a = 35 ^(2) - 27 ^(2)

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  12. Find the value of a, if 9a = 76 ^(2) - 67 ^(2)

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  13. Find the value of a, if pqa = (3p + q) ^(2) - (3p - q) ^(2)

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  14. Find the value of a, if pq ^(2) a = (4pq + 3q) ^(2) - ( 4pq - 3q) ^(...

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  15. What should be added to 4c (– a + b + c) to obtain 3a (a + b + c) – 2b...

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  16. Subtract b (b ^(2) + b- 7) + 5 from 3b ^(2) - 8 and find the value of ...

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  17. If x - (1)/(x) = 7 then find value of x ^(2) + (1)/(x ^(2)).

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  18. Factorise x ^(2) + (1)/( x^(2)) + 2 - 3x - (3)/(x).

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  19. Factorise p ^(4) + q ^(4) + p ^(2) q ^(2).

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  20. Find the value of (6.25 xx 6.25 - 1. 75 xx 1. 75)/(4.5)

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