Will the product always increase? Find 3 examples where the product decreases. Class 8

Will the product always increase? Find 3 examples where the product decreases. Class 8

Question 1.

Will the product always increase? Find 3 examples where the product decreases. Class 8

Solution:

No. For example,

(i) (a + 2) (-3) = -3a - 6 decrease

(ii) (a + 3) (-5 + 3) = -2a - 6 decrease

(iii) (x + y) (3 — 8) = — 5x - 5y decrease

Note : Actual increase or decrease will depend on the values of x and y.

Question 2.

Use Identity 1 to find how the product changes when

(i) one number is decreased by 2 and the other increased by 3;

(ii) both numbers are decreased, one by 3 and the other by 4. Class 8

Solution:

(i) (a —2) (6 + 3) = ab + 3a - 2b - 6

So, there will be a change of 3a - 2b - 6 in the product. Increase or decrease will depend on the values of a and 6. If a = 5 and 6 = 1, then there will be an increase of 15 - 2 - 6 = 7.

If a = 2 and b = 7, then there will be decrease of 3 × 2 - 2 × 7 - 6 = 14.

(ii) (a - 3) (b - 4) = a6 - 4a - 36 + 12. So, there will be change of - 4a - 3b + 12 in the product. Increase or decrease will depend on the values of a and 6 as in the case of (i).