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 x^3
+ ax^2
– bx + 10 is divisible by x^2
– 3x + 2, find the values of a and b.
9. Using factor theorem, factorize each of the following polynomials:
(i) x^3
– 6x^2
+ 3x + 10
(ii) 2y^3
– 5y^2
– 19y + 42
10. Represent √ 3 on number line.
11. Visualise 2.3469 on number line.
12. Factorise 6x^2 +5x -6 by splitting the middle term and also by using factor theorem.
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