Question

Find the difference in the given questions.

(i) (125 × 75) – (126 × 74) 

(ii) (124 × 76) – (126 × 74) 

(iii) (224 × 176) – (226 × 174) 

(iv) (10.3 × 9.7) – (10.7 × 9.3) 

(v) (11.3 × 10.7) – (11.7 × 11.3)

Answer 1

(i) (125 × 75) – (126 × 74)

(100 + 25) (100 – 25) – (100 + 26) (100 – 26)

(100² – 25²) – (100² – 26²)

= 26² – 25²

= (26 + 25) (26 – 25)

= 51

(ii) (124 × 76) – (126 × 74)

(100 + 24) (100 – 24) – (100 + 26) (100 – 26)

(100² – 24²) – (100² – 26)²

= 26² – 24² 

= (26 + 24) (26 – 24) 

= 50 × 2 

= 100 

(iii) (224 × 176) – (226 × 174) 

(200 + 24) (200 – 24) – (200 + 26) (200 – 26) 

(200² – 24²) – (200² – 26²) 

= 26² – 24² 

= (26 + 24) (26 – 24) 

= 50 × 2 

= 100 

(iv) (10.3 × 9.7) – (10.7 × 9.3)

(10 + 0.3) (10 – 0.3) – (10 + 0.7) (10 – 0.7)

(10² – 0.3²) – (10² – 0.7²).

= 0.7² – 0.3²

= (0.7 + 0.3) (0.7 – 0.3)

= 1 × 4 = 4

(v) (11.3 × 10.7) – (11.7 × 11.3)

(11 + 0.3) (11 – 0.3) – (11 + 0.7) (11 – 0.7)

(11² – 0.3²) – (11² – 0.7²)

= 0.7² – 0.3²

= (0.7 + 0.3) (0.7 – 0.3)

= 1 × 0.4 = 0.4