Mathematics
Assertion (A): a(2x - 3y) + b(3y - 2x)2 = a(2x - 3y) - b(2x - 3y)2
Reason (R): +b(3y - 2x)2 is not equal to -b(2x - 3y)2.
- A is true, R is false.
- A is false, R is true.
- Both A and R are true.
- Both A and R are false.
Factorisation
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Answer
A is false, R is true.
Explanation
L.H.S.
= a(2x - 3y) + b(3y - 2x)2
= 2xa - 3ya + b(9y2 + 4x2 - 12xy)
= 2xa - 3ya + 9y2b + 4x2b - 12xyb
R.H.S.
= a(2x - 3y) - b(2x - 3y)2
= 2xa - 3ya - b(4x2 + 9y2 - 12xy)
= 2xa - 3ya - 4x2b - 9y2b + 12xyb
L.H.S. ≠ R.H.S.
∴ Assertion (A) is false.
Taking L.H.S.
= +b(3y - 2x)2
= b(9y2 + 4x2 - 12xy)
= 9y2b + 4x2b - 12xyb
R.H.S.
= -b(2x - 3y)2
= -b(4x2 + 9y2 - 12xy)
= -4x2b - 9y2b + 12xyb
L.H.S. ≠ R.H.S.
∴ Reason (R) is true.
Hence, Assertion (A) is false, Reason (R) is true.
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