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A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

# Using a^{2} - b^{2} = (a + b)(a - b), find

(i) 51^{2} – 49^{2 }(ii) (1.02)^{2} - (0.98)^{2 }(iii) 153^{2} -147^{2 }(iv) 12.1^{2} - 7.9^{2}

**Solution:**

We will be solving the questions using the algebraic identity a^{2} - b^{2} = (a + b)(a - b)

(i) 51^{2} – 49^{2}

= (51 + 49)(51 - 49)

= (100)(2)

= 200

(ii) (1.02)^{2} - (0.98)^{2}

= (1.02 + 0.98)(1.02 - 0.98)

= (2)(0.04)

= 0.08

(iii) 153^{2} - 147^{2}

= (153 + 147)(153 - 147)

= (300)(6)

= 1800

(iv) 12.1^{2} - 7.9^{2}

= (12.1 + 7.9)(12.1 - 7.9)

= (20.0)(4.2)

= 84

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

**Video Solution:**

## Using a² - b² = (a + b)(a - b), find (i) 51² – 49² (ii) (1.02)² - (0.98)² (iii) 153² -147²^{ }(iv) 12.1² - 7.9²

NCERT Solutions Class 8 Maths Chapter 9 Exercise 9.5 Question 7

**Summary:**

Using a^{2} - b^{2} = (a + b)(a - b), the value of the following expressions (i) 51^{2} – 49^{2 } (ii) (1.02)^{2} - (0.98)^{2} (iii) 153^{2} -147^{2 }(iv) 12.1^{2} - 7.9^{2} are i) 200 ii) 0.08 iii) 1800 iv) 84

**☛ 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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