Question

EXPANSION QUESTIONS

By using standard formulae, expand the following (1-9):

1. (i) (2x + 7y)2

2. (ii) (3x2y + 5z)2

3. (i) (3x – 1/2x)2

4. (i) (x + 3) (x + 5)

(ii) (x + 3) (x – 5)

(iii) (x – 7) (x + 9)

5. (i) (x – 2y – z)2

(ii) (2x – 3y + 4z)2

6. (i) (2x + 3/x – 1)2

(ii) (2/3 x – 3/2x – 1)2

7. (i) (x + 2)3

(ii) (2a + b)3

8. (i) (3x + 1/x)3

9. (i) (5x – 3y)3

 

 

Simplify the following (10 to 19):

10. (i) (a + b)2 + (a – b)2

(ii) (a + b)2 – (a – b)2

11. (i) (a + 1/a)2 + (a – 1/a)2

(ii) (a + 1/a)2 – (a – 1/a)2

12. (i) (3x – 1)2 – (3x – 2) (3x + 1)

13. (i) (7p + 9q) (7p – 9q)

(ii) (2x – 3/x) (2x + 3/x)

14. (i) (2x – y + 3) (2x – y – 3)

(ii) (3x + y – 5) (3x – y – 5)

15. (i) (x + 2/x – 3) (x – 2/x – 3)

16. (i) (x + 2y + 3) (x + 2y + 7)

(ii) (2x + y + 5) (2x + y – 9)

17. (i) (2p + 3q) (4p2 – 6pq + 9q2)

(ii) (x + 1/x) (x2 – 1 + 1/x2)

18. (i) (3p – 4q) (9p2 + 12pq + 16q2)

(ii) (x – 3/x) (x2 + 3 + 9/x2)

19. (2x + 3y + 4z) (4x2 + 9y2 + 16z2 – 6xy – 12yz – 8zx).

21. Find the coefficient of x2 and x in the product of (x – 3) (x + 7) (x – 4).

22. If a2 + 4a + x = (a + 2)2, find the value of x.

23. Use (a + b)2 = a2 + 2ab + b2 to evaluate the following:

(i) (101)2

(ii) (1003)2

24. Use (a – b)2 = a2 – 2ab – b2 to evaluate the following:

(i) (99)2

(ii) (997)2

25. By using suitable identities, evaluate the following:

(i) (103)3

(ii) (99)3

27. If a + b + 2c = 0, prove that a3 + b3 + 8c3 = 6abc.

28. If a + b + c = 0, then find the value of a2/bc + b2/ca + c2/ab.

29. If x + y = 4, then find the value of x3 + y3 + 12xy – 64.

30. Without actually calculating the cubes, find the values of:

(i) (27)3 + (-17)3 + (-10)3

(ii) (-28)3 + (15)3 + (13)3

1. If x – y = 8 and xy = 5, find x2 + y2.

2. If x + y = 10 and xy = 21, find 2 (x2 + y2).

3. If 2a + 3b = 7 and ab = 2, find 4a2 + 9b2.

4. If 3x – 4y = 16 and xy = 4, find the value of 9x2 + 16y2.

5. If a2 + b2 = 13 and ab = 6, find

(i) a + b

(ii) a – b

6. If x – 3 = 1/x, find the value of x2 + 1/x2.

7. If x + y = 8 and xy = 3 ¾, find the values of

(i) x – y

(ii) 3 (x2 + y2)

(iii) 5 (x2 + y2) + 4 (x – y).

8. If x2 + y2 = 34 and xy = 10 ½, find the value of 2 (x + y)2 + (x – y)2.

9. If a – b = 3 and ab = 4, find a3 – b3.

10. If 2a – 3b = 3 and ab = 2, find the value of 8a3 – 27b3.

11. If x + 1/x = 4, find the values of

(i) x2 + 1/x2

(ii) x4 + 1/x4

(iii) x3 + 1/x3

(iv) x – 1/x.

12. If x – 1/x = √5, find the values of

(i) x2 + 1/x2

(ii) x + 1/x

(iii) x3 + 1/x3

13. If x + 1/x = 6, find

(i) x – 1/x

(ii) x2 – 1/x2.

14. If a + 2b = 5, prove that a3 + 8b3 + 30ab = 125.

15. If a2 – 3a + 1 = 0, find

(i) a2 + 1/a2

(ii) a3 + 1/a3.

16. If a + b + c = 12 and ab + bc + ca = 22, find a2 + b2 + c2.

17. If a + b + c = 12 and a2 + b2 + c2 = 100, find ab + bc + ca.

18. If a2 + b2 + c2 = 125 and ab + bc + ca = 50, find a + b + c.

19. If a + b – c = 5 and a2 + b2 + c2 = 29, find the value of ab – bc – ca.

20. If a – b = 7 and a2 + b2 = 85, then find the value of a3 – b3.

21. If the sum and the product of two numbers are 8 and 15 respectively, find the sum of their cubes.​

Answer 1

Answer:

the sum and the product of two numbers are 8 and 15 respectively, find the sum of their cubes