3. Factorise the following using appropriate identities:
(i) (9x^2+6xy+y^2)
(ii) (4y^2-4y+1)
(iii) (x^2-{y^2over 100})
Polynomials
Exercise 2.4
Class 9
Polynomials
Exercise 2.4
1. Use suitable identities to find the following products:
(iv) ((y^2+{3over 2})(y^2-{3over 2}))
2. Evaluate the following products without multiplying directly:
3. Factorise the following using appropriate identities:
4. Expand each of the following, using suitable identities:
(vi) ([{1over 4}a-{1over 2}b+1]^2)
(i) (4x^2+9y^2+16z^2+12xy-24yz-16xz)
(ii) (2x^2+y^2+8z^2-2sqrt 2 xy+4sqrt 2 yz-8xz)
6. Write the following cubes in expanded form:
7. Evaluate the following using suitable identities:
8. Factorise each of the following :
(iv) (64a^3-27b^3-144a^2b+108ab^2)
(v) (27p^3-{1over 216}-{9over 2}p^2+{1over 4}p)
(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 :
11. Factorise : (27x^3+y^3+z^3-9xyz)
12. Verify that (x^3+y^3+z^3-3xyz=)({1over 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:
(ii) Volume : (12ky^2+8ky-20k)
