The number which should be subtracted from 5a2-3ab+7b2 to make it equal to…

To find the number that must be subtracted from an expression P to obtain a target expression Q, set up P minus the unknown X equals Q, so X equals P minus Q. Subtract the target's like-term coefficients from the original's like-term coefficients to get X.

1. Let X be the number to be subtracted. Set up the equation: (5a2-3ab+7b2) - X = a2+ab+b2

2. Rearrange to isolate X: X = (5a2-3ab+7b2) - (a2+ab+b2)

3. Subtract the a2 terms: 5a2 - a2 = 4a2

4. Subtract the ab terms: -3ab - ab = -4ab

5. Subtract the b2 terms: 7b2 - b2 = 6b2

6. Combine the results: X = 4a2 - 4ab + 6b2

Cross-check: add X back to the target expression: (a2+ab+b2) + (4a2-4ab+6b2) = 5a2-3ab+7b2, which matches the original expression, confirming X is correct.

Therefore, the required number is 4a2-4ab+6b2.