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1 9. Algebraic Expressions and Identities Q 1 Using identity (x - a) (x + a) = x 2 a 2 find Q 2 Find the product of (7x 4y) and (3x - 7y). Q 3 Using suitable identity find (a + 3)(a + 2). Q 4 Using identity (a + b) 2 = a 2 + 2ab + b 2 find the value of Q 5 Using identity (a b) 2 = a 2 2ab + b 2 find the value of Q 6 Using identity find (2x +3) 2. Q 7 Subtract 7x - 3x 2 from 4x + 8x 2. Q 8 Using suitable identity find (7x - 3y) 2. Q 9 Add 4x 2 + 2xy 4 and 7x 2 3xy + 4. Q 10 Find the product of 4x, 7x 2, -2x. Q 11 Find the product of (x 2 y 2 )(2x + y). Q 12 Simplify: (xy + yz) 2 (xy yz) 2 Q 13 Using identity find the product of Q 14 Multiply: (a 2 + 2c 2 ) (3a 3c) Q 15 Simplify: (x + y) (2x 3y + z) (2x 3y)z
2 Q 16 Subtract 3x (x 4y + 5z) from 4x (2x 3y + 10z). Q 17 Simplify: (x 2 y 2 ) 2 Q 18 Using suitable identity find the product of. Q 19 Simplify 3a(4a - 5) + 3 and find its value for a = 3. Q 20 Using suitable identity find (6x 2 5/3) 2. Q 21 Using identity a 2 - b 2 = (a + b) (a b), find (1.02) 2 (0.98) 2. Q 22 Using (x + a) (x + b) = x 2 + (a +b) x + ab find Q 23 Using identity find the value of (7.2) 2. Q 24 Using identity evaluate Q 25 Using identity find the value of (4.7) 2. Q 26 Marks (4) Q 27 Simplify (xy + yz) 2 2x 2 y 2 z. Find the value when x = -1, y = 1 and z = 2. Marks (4) Q 28 Simplify: (1.5x 4y)(1.5x + 4y +3) 4.5x +12y Marks (4)
3 Most Important Questions Q 1 What are algebraic expressions? Q 2 Expressions consists of &. Q 3 T/F. The value of an expression changes with the value chosen for the variables it contains. Q 4 When numbers/literals are added or subtracted, they are called. Q 5 When numbers/literals are multiplied, they are called. Q 6 The terms in the expression 4ab + 5a(b + c) are: Q 7 The factors in the term 5a(b + c) are : Q 8 A monomial is an expression in which. Q 9 A binomial is an expression in which. Q 10 While multiplying two monomials, Coefficient of product = X. Q 11 Identify the terms, their coefficients for the expression: 0.75x y zx Q 12 Classify the following as binimials and trinomials: 2a + 3b, 2x+3y-5, a+4, 12x+13y+17z Q 13 What are the polynomials? Give an example. Q 14 What are like and unlike terms? Q 15 Classify as like and unlike terms: 2abc and bac, x 2 y 2 z and y 2 zx 2. 7x and 3y xy+z and xyz
4 Q 16 Add: 2p 2 q 2 3pq + 4 & 5 + 7pq 3p 2 q 2 Q 17 Q 18 Q 19 Find the product of : 2z, 4y, 2y 2 & 6xyz Q 20 Find : a) 13mn 13np b) -4xy -7x 2 y Q 21 State the distributive property. Q 22 T/F: n ( 4 + m) = 4n + nm Q 23 T/F : p( 9 p) = 9p 2p Q 24 Whenever we multiply a binomial by a binomial, we get terms in the product. Q 25 Whenever we multiply a binomial by a trinomial, we get terms in the product. Q 26 Find : a 2 (2ab - 5c) Q 27 Simplify x(x - 3) + 2 and evaluate for x= 2. Q 28 Q 29
5 Q 30 Find using distributive property : 125 X 42 Q 31 Find : ab(a 2 + bc + c 2 ) Q 32 Q 33 Q 34 Multiply : (ab + 5)(a + c 2 )(b + 6) Q 35 Simplify : (m + n)(3m + n) + (m + 2n)((m - n) Q 36 Simplify: (3.5e - 4.5f)(1.5e + 4f + ef) - 4.5e + 10f Q 37 Simplify : (3.5e - 4.5f)(1.5e + 4f + ef) - 4.5e + 10f Q 38 What is an identity. Q 39 True/False An equation, which is true for only certain values of the variable in it, is not an identity. Q 40 (x + a)(x + b) = Q 41 (a - b) 2 =
6 Q 42 (x - a)(x + a) =. Q 43 Q 44 Q 45 Find using identities:106 2 Q 46 Find using identities: (4.8) 2 Q 47 Find using identities: ( p + q) ( p + q) Q 48 Find : (2x + 5y) (2x + 3y) Q 49 Find : (2x - y)(2x + y)(4x 2 + y 2 ) Q 50 Multiply : [ p 2 + (qr) 2 ] [ p 2 - (qr) 2 ] and evaluate for p = 1, q = 2, r = 3. Q 51 Derive the identity : (x + a)(x + b) = x 2 + (a + b)x + ab Q 52 Find the product :
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