Question

1. If x + y = 12 and xy = 32, Find the value of x2

+ y2


2. If 3x + 2y = 12 and xy = 6, find the value of 9x2

+ 4y2

3. Write the following cubes in the expanded form:

(i) (3a + 4b)3.

(ii) (5p – 3q)3

6. If a + b + c = 15 and a2

+ b2

+ c2

= 83, find the value of a3

+ b3

+ c3

– 3abc.

7. Factorize:

(i) 6ab – b

2

+ 12ac – 2bc

(ii) 9(2a – b)2

– 4(2a – b) – 13

8. If x3

+ ax2

– bx + 10 is divisible by x2

– 3x + 2, find the values of a and b.

9. Using factor theorem, factorize each of the following polynomials:

(i) x3

– 6x2

+ 3x + 10

(ii) 2y3

– 5y2

– 19y + 42

10. Represent √ 3 on number line.

11. Visualise 2.3469 on number line.

12. Factorise 6x2 +5x -6 by splitting the middle term and also by using factor theorem.​

Answer 1

Answer:

1. 144

2. 144

3. (3a)3 +(4b)3 +3×3a×4b(3a+4b)

=> 27a^3 + 64b^3 +36ab (3a+4b)

=> 27a^3 + 64b^3 +108a^2b+144ab^2