1.

Use the identity (x + a) (x + b) = x2 + (a + b) x + ab to find the following products:(i) (x + 1) (x + 2)(ii) (3x + 5) (3x + 1)(iii) (4x – 5) (4x – 1)(iv) (3a + 5) (3a – 8)(v) (xyz – 1) (xyz – 2)

Answer»

(i) (x + 1) (x + 2)
= x2 + (1 + 2)x + 1 × 2 (Using given identity)
= x2 + 3x + 2

(ii) (3x + 5) (3x + 1)
= (3x)2 + (5 + 1) 3x + 5 x 1 (Using given identity)
= 9x2 + 18x + 5

(iii) (4x – 5) (4x – 1)
= {4x + (- 5)} {4x + {- 1)}
= (4x)2 + {(- 5) + (- 1)} 4x + (- 5) (- 1) (Using given identity)
= 16x2 + (- 6) 4x + (5)
= 16x2 – 24x + 5

(iv) (3a + 5) (3a – 8)
= (3a + 5) {3a + (- 8)}
= (3a)2 + {5 + (- 8)} 3a + (5) (- 8) (Using given identity)
= 9a2 + (- 3) 3a – 40
= 9a2 – 9a – 40

(v) {xyz – 1) (xyz – 2)
= {xyz + {- 1)} {xyz + {- 2)}
= {xyz)2 + {(- 1) + (- 2)} xyz + (- 1) (- 2)
= x2y2z2 – 3xyz + 2


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