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## Ncert Solutions for Class 9

#### Exercise 2.4

1. Use suitable identities to find the following products:

(i) (x + 4) (x + 10)

(ii) (x + 8) (x – 10)

(iii) (3x + 4) (3x – 5)

(iv) $$(y^2+{3\over 2})(y^2-{3\over 2})$$

(v) $$(3-2x)(3+2x)$$

2. Evaluate the following products without multiplying directly:

(i) 103 × 107

(ii) 95 × 96

(iii) 104 × 96

3. Factorise the following using appropriate identities:

(i) $$9x^2+6xy+y^2$$

(ii) $$4y^2-4y+1$$

(iii) $$x^2-{y^2\over 100}$$

4. Expand each of the following, using suitable identities:

(i) $$(x+2y+4z)^2$$

(ii) $$(2x-y+z)^2$$

(iii) $$(-2x+3y+2z)^2$$

(iv) $$(3a-7b-c)^2$$

(v) $$(-2x+5y-3z)^2$$

(vi) $$[{1\over 4}a-{1\over 2}b+1]^2$$

5. Factorise :

(i) $$4x^2+9y^2+16z^2+12xy-24yz-16xz$$

(ii) $$2x^2+y^2+8z^2-2\sqrt 2 xy+4\sqrt 2 yz-8xz$$

6. Write the following cubes in expanded form:

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

(ii) $$(2a-3b)^3$$

(iii) $$[{3\over 2}x+1]^3$$

(iv) $$[x-{2\over 3}y]^3$$

7. Evaluate the following using suitable identities:

(i) $$(99)^3$$

(ii) $$(102)^3$$

(iii) $$(998)^3$$

8. Factorise each of the following :

(i) $$8a^3+b^3+12a^2b+6ab^2$$

(ii) $$8a^3-b^3-12a^2b+6ab^2$$

(iii) $$27-125a^3-135a+225a^2$$

(iv) $$64a^3-27b^3-144a^2b+108ab^2$$

(v) $$27p^3-{1\over 216}-{9\over 2}p^2+{1\over 4}p$$

9. Verify :

(i) $$x^3+y^3=$$$$(x+y)(x^2-xy+y^2)$$

(ii) $$x^3-y^3=$$$$(x-y)(x^2+xy+y^2)$$

10. Factorise each of the following :

(i) $$27y^3+125z^3$$

(ii) $$64m^3-343n^3$$

11. Factorise : $$27x^3+y^3+z^3-9xyz$$

12. Verify that $$x^3+y^3+z^3-3xyz=$$$${1\over 2}(x+y+z)$$$$[(x-y)^2+(y-z)^2+(z-x)^2]$$

13. If $$x+y+z=0$$, show that $$x^3+y^3+z^3=3xyz$$.

14. Without actually calculating the cubes, find the value of each of the following:

(i) $$(-12)^3+(7)^3+(5)^3$$

(ii) $$(28)^3+(-15)^3+(-13)^3$$

15. Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:

(i) Area : $$25a^2-35a+12$$

(ii) Area : $$35y^2+13y-12$$

16. What are the possible expressions for the dimensions of the cuboids whose volumes are given below?

(i) Volume : $$3x^2-12x$$

(ii) Volume : $$12ky^2+8ky-20k$$