# Using (x + a)(x + b) = x^{2} + (a + b)x + ab

(i) 103 × 104 (ii) 5.1 × 5.2 (iii) 103 × 98 (iv) 9.7 × 9.8

**Solution:**

We will be using the algebraic Identity (x + a)(x + b) = x^{2} + (a + b)x + ab

(i) 103 × 104

= (100 + 3)(100 + 4)

= (100)^{2} + (3 + 4)(100) + (3)(4)

= 10000 + 700 + 12

= 10712

(ii) 5.1 × 5.2

= (5 + 0.1)(5 + 0.2)

= (5)^{2} + (0.1 + 0.2)(5) + (0.1)(0.2)

= 25 + 1.5 + 0.02

= 26.52

(iii) 103 × 98

= (100 + 3)(100 - 2)

= (100)^{2} + [3 + (-2)](100) + (3)(-2)

= 10000 + 100 - 6

= 10094

(iv) 9.7 × 9.8

= (10 - 0.3)(10 - 0.2)

= (10)^{2} + [(-0.3) + (-0.2)](10) + (-0.3)(-0.2)

= 100 + (- 0.5)10 + 0.06

= 100 - 5 + 0.06

= 95.06

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 9

**Video Solution:**

## Using (x + a)(x + b) = x² + (a + b)x + ab (i) 103 × 104 (ii) 5.1 × 5.2 (iii) 103 × 98 (iv) 9.7 × 9.8

NCERT Solutions Class 8 Maths Chapter 9 Exercise 9.5 Question 8

**Summary:**

Using (x + a)(x + b) = x^{2} + (a + b)x + ab the following expressions (i) 103 × 104 (ii) 5.1 × 5.2 (iii) 103 × 98 (iv) 9.7 × 9.8 are evaluated as follows i) 10712 ii) 26.52 iii) 10094 iv) 95.06

**☛ Related Questions:**

- Use a suitable identity to get each of the following products. (i) (x + 3)(x + 3) (ii) (2y + 5)(2y + 5) (iii) (2a - 7)(2a - 7) (iv) (3a - (1/2))(3a - (1/2)) (v) (1.1 m - 0.4)(1.1 m + 0.4) (vi)(a2 + b2)(-a2 + b2) (vii) (6x - 7)(6x + 7) (viii) (-a + c)(-a + c) (ix) (x/2 + 3y/4)(x/2 + 3y/4) (x) (7a - 9b)(7a - 9b)
- Use the identity (x + a)(x + b) = x2 + (a + b)x + ab to find the following products. (i) (x + 3)(x + 7) (ii) (4x + 5)(4x + 1) (iii) (4x - 5)(4x -1) (iv) (4x + 5)(4x -1) (v) (2x + 5y)(2x + 3 y) (vi) (2a2 + 9)(2a2 + 5) (vii) (xyz - 4)(xyz - 2)
- Find the following squares by using the identities. (i)(b - 7)2 (ii) (xy + 3z)2 (iii) (6x2 - 5 y)2 (iv) (2m/3 + 3n/2)2 (v) (0.4 p - 0.5q)2 (vi) (2xy + 5 y)2
- Simplify (i)(a2 - b2)2 (ii) (2x + 5)2 - (2x - 5)2 (iii) (7m - 8n)2 + (7m + 8n)2 (iv) (4m + 5n)2 + (5m + 4n)2 (v) (2.5p - 1.5q)2 - (1.5p - 2.5q)2 (vi) (ab + bc)2 - 2ab2c (vii) (m2 - n2m)2 + 2m3n2

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