Class 9
Polynomials
Exercise 2.4
1. Use suitable identities to find the following products:
(iv) \((y^2+{3\over 2})(y^2-{3\over 2})\)
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) \([{1\over 4}a-{1\over 2}b+1]^2\)
(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:
7. Evaluate the following using suitable identities:
8. Factorise each of the following :
(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) \(27p^3-{1\over 216}-{9\over 2}p^2+{1\over 4}p\)
(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 \(x^3+y^3+z^3-3xyz=\)\({1\over 2}(x+y+z)\)\([(x-y)^2+(y-z)^2+(z-x)^2]\)
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: