**Find the product of the following:**

(i) (x + 1) (x + 2) (x + 3)

(ii) (x – 2) (x – 3) (x + 4)

**Answer :**

**(i) (x + 1) (x + 2) (x + 3)**

It can be written as

= x^{3} + (1 + 2 + 3)x^{2} + (1 × 2 + 2 × 3 + 3 × 1) x + 1 × 2 × 3

By further calculation

= x^{3} + 6x^{2} + (2 + 6 + 3)x + 6

So we get

= x^{3} + 6x^{2} + 11x + 6

**(ii) (x – 2) (x – 3) (x + 4)**

It can be written as

= x^{3} + (- 2 – 3 + 4) x^{2} + [(-2) × (-3) + (-3) × 4 + 4 × (-2)]x + (-2) (-3) (4)

By further calculation

= x^{3} – x^{2} + (6 – 12 – 8)x + 24

= x^{3} – x^{2} – 14x + 24

**More Solutions:**

- Without actually calculating the cubes, find the values of:
- Using suitable identity, find the value of:
- If x – y = 8 and xy = 5, find x2 + y2.
- If x + y = 10 and xy = 21, find 2 (x2 + y2).
- If 2a + 3b = 7 and ab = 2, find 4a2 + 9b2.
- Find the value of 9×2 + 16y2.
- Find the value of 2×2 + 2y2.
- If a2 + b2 = 13 and ab = 6, find
- If a + b = 4 and ab = -12, find
- If p – q = 9 and pq = 36, evaluate