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Question

What should be subtracted from 2a+8b+10 to get 3a+7b+16

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Solution

Let the value to be subtracted from 2a+8b+10 to get 3a+7b+16 be xa+yb+z.
Therefore,
(2a+8b+10)(xa+yb+z)=3a+7b+16
(2x)a+(8y)b+10z=3a+7b+16
On comparing coefficients,
2x=3x=5
8y=7y=1
10z=16z=6
Hence, the required value is 5a+b6.

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