Algebraic Expressions Exercise # 1

EXERCISE # 1 Q.1 If a letter has no coefficient written before it, the coefficient _______is understood. (A) 0 (B) 1 (C) –1 (D) None of these Q.2 The terms whose literal factors are same are called _______ terms. (A) like (B) unlike (C) monomial (D) None of these Q.3 If m = 2, then value of 9 – 5m is (A) 1 (B) 0 (C) –1 (D) 2 Q.4 Identify monomials, binomials and trinomials from the following expressions : (i) y3 + 2 (ii) 9x2y (iii) 2 – a2 – 2b2 (iv) 6a2b2 – 8ab –5ab Q.5 Q.7 Q.8 Q.9 Simplify combining like terms : (i) a – (a – b) – b – (2b – a) (ii) 2x –3y –2xy – (2x –3y + xy) + 6xy + y – x Q.11 Simplify the expressions and find their value if x is equal to 3. (i) 3(3x – 1) + 4x + 9 (ii) 6x + 4 + 3 (4x – 8) Q.12 Add the following terms : (i) x2y, 6x2y, –8x2y (ii) ab2, –2ab2, 8ab2, 14ab2 Q.13 Add the following terms : (i) 5x –6y, 8x + 7y, –4x + 3y (ii) 6x3 + 8 + 7x – 8x2, 3x2 – 9 – 8x, 3x – x2 + 2x3 Q.14 Subtract : (i) x3 + 3x2y + 6xy2 –2y3 from y3 –4xy2 –5x2y (ii) 7x3 –9x2 + 5x – 3 from 6 – 5x + 7x2 – 9x3 Q.15 What should be added to 2a2 + ab + b2 to get 3a2 + 4ab ? Q.16 What should be subtracted from 4a + 16b + 20 to get –11a + 2b – 26 ? Q.17 From the sum of a –3b + 12 and – a + 15, subtract 4a + b – 30. Q.18 From the sum of 6 + 4y + y2 and 8 – 5y + 3y2, subtract the sum of 6y2 – 4y and –y2 + 4y + 9. Write the coefficient of (i) x in – 6y2x (ii) a in –3a (iii) b in Q.6 Q.10 1 ba 5 (iv) x in – 5xy2 Add 9 + x –2x2, 6 – x + 2x2 + 3x3, 4x3 – x – 8. 2 2 Subtract –4xy –2xy –5x y from the sum of –x2y + xy2 and 2xy + 4x2y. 3 2 To what expression must 4x –3x + 8x + 6 be added so as to make zero. If A = 2x2 –5x –7, B = x2 + 4x – 3, C = – 4x2 – 4x + 3, find A – B – C. ANSWER KEY 1. (B) 5. (i) –6y2 (ii) –3 8. –4x + 3x3 – 8x2 – 6 2. (A) (iii) 1 a 5 3. (C) (iv) –5y2 9. 5x2 – 5x – 7 11. (i) (13x + 6), 45 (ii) (18x – 20), 34 4. (i) Binomial (ii) Monomial 6. 7 – x + 7x3 (iii) Trinomial (iv) Binomial 7. 8x2y + 4xy + 5xy2 10. (i) –2b + a (ii) –x + 3xy + y 12. (i) –x2y (ii) 21ab2 13. (i) 9x + 4y (ii) 8x3 – 6x2 + 2x – 1 14. (i) 3y3 – 10xy2 – 8x2y – x3 (ii) 9 – 10x + 16x2 – 16x3 16. 15a + 14b + 46 15. a2 + 3ab – b2 18. –y2 – y + 5 17. –4a – 4b + 57 EXERCISE # 2 Q.1 Q.2 Q.3 Q.4 Get the algebraic expressions in the following cases using variables, constants and arithmetic operations : (i) Add twice of x and y (ii) Subtract y from thrice of x (iii) One-third of the product of a and b (iv) Square of x is subtracted from square of y (v) Subtract 25 from the sum of a and b Classify the following expressions as Monomial, Binomial, Trinomial : (i) 2x + 7 (ii) 5a2b + 3ab2 (iii) 0 (iv) –6x + by –9z2 Identify the monomials, binomials and trinomials from the following expressions : (i) 5x2 (ii) x3 – 1 (iii) x2 – y2 (iv) 4x2 – 3y + 3 (v) 3x2 + 2x + 5 (vi) – xyz 3 3 (vii) a + b –3ab (viii) 3x – z Q.8 Add the following : (i) The length of a rectangle is x2 – x and its width is x – 4. Find its perimeter. 2 2 1  2  (ii)  y 2 − y + 5  −  y − y 2 + 2  4 3 3  7  1  and −  y − 3 + 2 y 2  7  Q.9 Simplify each of the expression : (i) Q.10 Subtract the lower expression from the upper expression and check : (i) 7 2 2 3 xyz 8 (v) x in –3xy2z (ii) (iv) x2 in x3 – 2x + 3 (vi) p in –3pq3r4 Q.5 Write the numerical coefficient of each of the following : (i) xy (ii) – 6yz (iii) 7abc (iv) –2x3y2z Q.6 Write the numerical coefficient of each term in the following expression : –2x2y2 – 1 4 xy + z 5 Identify like terms in each of the following : (i) x3, y2, 2x3, z2 (ii) 3xy, yz, 4x, yz 2 1 1 1 a− a+ a 2 3 4 (ii) (a + b – c) + (b + c – a) + (c + a – b) (iii) 2b – a – b – 2c – b + a – (a – b – c) Write the coefficient of : (i) x in (–2x) (ii) 5 in 5abc (iii) y2 in Q.7 (iii) –2x2y, x2z, – yx2, x2y2 (iv) cab2, a2bc, b2ac2, c2ab, a2b2c, abc, acb2 3x 3 − 7 x 2 + 4 x − 10 2 x 3 + 5x 2 − 6 x + 2 − 5a 2 − 7a + 8 3a 2 − 7a + 8 Q.11 Subtract the first expression from the second : (i) –5x2 – y2, 4x2 + y2 (ii) 5x2 + 3x, 5x2 – 3x Q.12 How much is x + 2y –3z greater than – x – y – 5z ? Q.13 Subtract the sum of (8a – 6a2 + 9) and (–10a – 8 + 8a2) from –3. Q.14 How much less than x – 4y + 3z is 3x – 6y – z ? Q.15 What must be added to 6x – 4y + 3z to obtain 3x – 2y + 7z ? Q.16 By how much does – 4a2b – 3ab2 + b2 exceed a3 + 2a2b + 6ab2 – b2 ? Q.17 The perimeter of a triangle is 7x – 10. One of the sides is x – 6, and another is 3x + 2. Find the third side. Q.18 The sum of two expressions is x2 – y2 – 2xy + y – 7. If one of them is 2x2 + 3y2 – 7y + 1. Find the other. Q.26 20x – [15x3 +5x2 – {8x2 – (4 – 2x – x3) – 5x3} –2x] Q.27 2a – 3b – [3a – 2b – {a – c – (a – 2b)}] From the sum of 3x – y + z and – y – z, subtract 3x – y –z. What is the coefficient of x in the result ? Q.28 – 4x2 + {(2x2 – 3) – (4 – 3x2)} Q.29 2a – [4b – {4a – (3b – 2a + 2b) }] Q.30 What is the value of 4x + x – 2x2 + x – 1, if x=–1? Q.31 Find the value of the following expressions : Q.19 Q.20 3 2 What must be added to 5x – 2x + 6x + 7 to make the sum x3 + 3x2 – x + 1? Simplify the following (Q.21 to Q.29) : 1 [(a2 – 5b) – 2 {2a2 – (3c – 2b)}] 3 Q.21 a– Q.22 xy – [yz – zx – {yx – (zy – xz) – (xy – zy)}] Q.23 4x3 – [9x2 – {–5x3 – (2 – 7x2) + 6x}] (i) (x + y) 2 – (x – y)2, if x = (ii) (x – y)2 + 4xy, if x = 1 1 ,y= 2 4 1 ,y=2 3 Q.24 – a – [a + {a + b – 2a – (a – b)} – b] Q.25 x – [{zy – (5x + y – z) + 2x2} – (x2 – 3y)] (iii) (x + y)2 – (x2 + y2 + 2xy), if x = 1, y = –1 Q.25 x – [{zy – (5x + y – z) + 2x2} – (x2 – 3y)] (iv) (x2 – y2) – (x + y) (x – y), if x = –1.7, y = –3.9 Edubull ANSWER KEY 1 ab 3 (iv) y2 – x2 1. (i) 2x + y (ii) 3x – y (iii) 2. (i) Binomial (ii) Binomial (iii) Monomial (iv) Trinomial 3. (i) Monomial (ii) Binomial (iii) Binomial (vi) Monomial (vii) Trinomial (viii) Binomial 7 2 3 x z 8 (v) (a + b) – 25 (iv) Trinomial (v) –3y2z (vi) –3q3r4 4. (i) –2 (ii) abc (iii) 5. (i) 1 (ii) –6 (iii) 7 6. 1 Coefficient of x2y2 = –2, Coefficient of xy4 = − , Coefficient of z = 1 5 7. (i) x3 and 2x3 (ii) yz and 8. (i) 2x2 – 8 9. (i) 5 a 12 (ii) − y 2 − (iv) x (iv) –2 yz (iii) –2x2y and –yx2 (iv) cab2 and acb2 2 13 y+6 14 (ii) (a + b + c) (iii) – a + b – c 10. (i) x3 – 12x2 + 10x – 12 (ii) –8a2 11. (i) 9x2 + 2y2 (ii) –6x 12. 2x + 3y + 2z 13. 2a – 2a2 – 4 14. –2x + 2y + 4z 3 2 15. –3x + 2y + 4z 2 16. a + 6a b + 9ab – 2b 2 2 2 18. –x – 4y – 2xy + 8y – 8 3 (v) Trinomial 2 17. 3x – 6 19. z – y, Coff. of x = 0 20. –4x + 5x – 7x – 6 21. a2 + a + 3b – 2c 22. xy – yz + 2xz 23. –x3 – 2x2 + 6x – 2 24. –b 25. –x2 – 6x – zy – 2y – z 26. –19x3 + 3x2 + 24x – 4 27. b – c – a 28. x2 – 7 29. 8a – 5b 30. –9 31. (i) 1 2 (ii) 49 9 (iii) 0 (iv) 0