4. Divide a3+a®b3+a*b*+a2b®+b8 by aa1+a3b+a2b2+ab3+ba, 1. Simplify the following expressions (i) {2x+y-(x+2y)} × {3x −2y — (2x-3y)}, 3. Multiply 323+4x2y—xy2+4y3 by x-2y, 4. Divide a1-81 by a-3, and a2 by a2-x2 to 4 terms. (a−b x−b− c y) − (a+b x+b+c y) to ax+cy+b (x+y). 2. If a=2, find the numerical value of a2a-1+2aa- 3. The product of two algebraical expressions is 4a2b2+2 (3a-2b4) — ab (5a2 — 1162), and one of them is 3a2+2ab-b2; find the other. 5. Solve the equations 3 (i) 2 (x−8) + 2 (x-9)-5 (x−11)=7- — (x − 17), 3 4 3 8 1. If a=5, b=3, c=1, find the numerical values of (ii) 5ab2+9bc-2/3a+b-2c. 2. Add together 3a3 + a3b-2ab2+b3, 3ab2-2a2b+a3, a2b―ab2+363, and subtract half the sum from 4. Divide a3-b(a2+b) y+ab2 by ay-b, 6. A boy is one-third the age of his father, and has a brother one-sixth of his own age; the ages of all these amount to 50 years. Find the age of each. EXERCISE XIV. 1. Multiply together x2−x+1, x2+x+1, and x − x2+1, and divide 16+28+ 1 by the continued product. 2. Find the cube of x−2y+3z, and the fourth power of 2a2-3ax. 5. A man travelled 105 miles, and then found that if he had not travelled so fast by 2 miles an hour, he would have been 6 hours longer in performing the journey. Determine his rate of travelling. 6. Prove that (a+b)2 − (c + d)2 + (a + c)3 − (b + d)2 = 2 (a−d) (a+b+c+d). EXERCISE XV. 1. By what expression must a2-bc be multiplied that the product may be a3+ a2b+ a2c-abc-b2c-bc2? 2. Find the square of 3a3-5a2b+6ab2-2b3, and the cube of X a a 3. Extract the square root of x6 — 4x5 — 2x2+12x3+9x2. 4. Find the value of when (x+y+ z)(x + y − z) (x+z− y) (y+z−x), 5. Solve the equations 6. In a certain examination, three-fourths of a boy's marks were gained by translation, one-eighth by mathematics, and one-tenth by Latin prose: he also obtained one mark for French. How many marks did he obtain for each subject? 1. Simplify EXERCISE XVI. (i) 5a-7(b-c)-[6a-(3b+2c)+4c-{2a-(b+2c-a)}], (ii) (2a−x) (2b−y)+(a+2x) (b+2y)− 5 (ab + xy). |