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# Exercise 3.4 : Algebraic Identities

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Exercise 3.4 : Algebraic Identities

1. Expand the following:

(i) (x + 2y + 3z)2 (ii) (p + 2q + 3r)2 (iii) (2 p + 3)(2 p 4)(2 p 5) (iv) (3a + 1)(3a 2)(3a + 4)

2. Using algebraic identity, find the coefficients of x2 , x and constant term without actual expansion.

(i) (x + 5)(x + 6)(x + 7) (ii) (2x + 3)(2x 5)(2x 6)

3. If (x + a )(x +b)(x + c ) = x3 + 14x2 + 59x + 70 , find the value of

(i) a + b +c (ii) 1/a + 1/b + 1/c (iii) a2 + b2 +c2 (iv) a/bc + b/ac + c/ab

4. Expand:

(i) (3a − 4b)3  (ii) ( x + 1/y )3

5. Evaluate the following by using identities:

(i) 983 (ii) 10013

6. If (x + y + z) = 9 and (xy + yz + zx) = 26, then find the value of x2 + y2 + z 2 .

7. Find 27a 3 + 64b3, if 3a + 4b = 10 and ab = 2 .

8. Find x 3 -y3 , if x y = 5 and xy = 14 .

9. If a + 1/a = 6 , then find the value of a3 + 1/a3 .

10. If x2 + [1/x2] = 23 , then find the value of x + [1/x] and x3 + [1/ x3].

11. If (y – 1/y)3 = 27 , then find the value of y3 – [1/y3]

12. Simplify: (i) (2a + 3b + 4c )(4a2 + 9b2 +16c 2 6ab 12bc 8ca)

(ii) (x 2y + 3z )(x 2 + 4y 2 + 9z 2 + 2xy + 6yz 3xz)

13. By using identity evaluate the following:

(i) 73 − 103 + 33 (ii) 1 + 1/8 – 27/8

14. If 2x 3y 4z = 0 , then find 8x 3 − 27y3 − 64z 3.

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