polynomials

Question 14: Without actually calculating the cubes, find the value of each of the following: (i) (–123 + (7)3 + (5)3 (ii) (28)3 + (–15)3 + (–13)3 Question 13 Question 15 Prerequisite Algebraic Identities  

Question 13: If x + y + z = 0, show that x3 + y3 + z3 = 3xyz. Question 12 Question 14 Prerequisite Algebraic Identities  

Question 12: Verify that x3 + y3 + z3 – 3xyz = 1/2 (x + y + z) [ (x – y)2 + (y – z)2 + (z – x)2 ] Question 11 Question 13 Prerequisite Algebraic Identities  

Question 11: Factorise : 27×3 + y3 + z3 – 9xyz Question 10 Question 12 Prerequisite Algebraic Identities  

Question 10: Factorise each of the following: (i) 27y3 + 125z3 (ii) 64m3 – 343n3 [Hint : See Question 9.] Question 9 Question 11 Prerequisite Algebraic Identities  

Question 9: Verify : (i) x3 + y3 = (x + y) (x2 – xy + y2 ) (ii) x3 – y3 = (x – y) (x2 + xy + y2 ) Question 8 Question 10 Prerequisite Algebraic Identities  

Question 8: Factorise each of the following: (i) 8a3 + b3 + 12a2b + 6ab2 (ii) 8a3 – b3 – 12a2b + 6ab2 (iii) 27 – 125a3 – 135a + 225a2 (iv) 64a3 – 27b3 – 144a2b + 108ab2 (v)…

Question 7: Evaluate the following using suitable identities: (i) (99)3 (ii) (102)3 (iii) (998)3 Question 6 Question 8 Prerequisite Algebraic Identities  

Question 6: Write the following cubes in expanded form: (i) (2x + 1)3 (ii) (2a – 3b)3 (iii) (3/2 x + 1)3 (iv) (x – 2/3 y)3 Question 5 Question 7 Prerequisite Algebraic Identities