Question

Simplify the following using the formula: (a-b)(a+b)=a² - b²:

(i) (82)²-(18)²

(ii) (467)²-(33)²

(iii) (79)²-(69)²

(iv) 197 x 203

(v) 113 x 87

(vi) 95 x 105

(vii) 1.8 x 2.2

(viii) 9.8 x 10.2

Answer 1

(i) (82)²- (18)²

Using formula:

(a – b) (a + b) = a² – b², we get

= (82 – 18) (82 + 18)

= 64 × 100

= 6400

(ii) (467)²- (33)²

Using formula:

(a – b) (a + b) = a² – b², we get

= (467 – 33) (467 + 33)

= (434) (500)

= 217000

(iii) (79)²- (69)²

Using formula:

(a – b) (a + b) = a² – b², we get

= (79 + 69) (79 – 69)

= (148) (10)

= 1480

(iv) 197 x 203

Using formula:

(a – b) (a + b)

= a² – b², we get

= (200 – 3) (200 + 3)

= (200)² – (3)²

= 40000 – 9

= 39991

(v) 113 x 87

Using formula:

(a – b) (a + b) = a² – b², we get

= (100 + 3) (100 – 3)

= (100)² – (3)²

= 10000 – 9

= 9991

(vi) 95 x 105

Using formula:

(a – b) (a + b) = a² – b², we get

= (100 – 5) (100 + 5)

= (100)² – (5)²

= 10000 – 25

= 9975

(vii) 1.8 x 2.2

Using formula:

(a – b) (a + b) = a² – b², we get

= (2- 0.2) (2 + 0.2)

= (2)² – (0.2)²

= 4 – 0.04

= 3.96

(viii) 9.8 x 10.2

Using formula:

(a – b) (a + b) = a² – b², we get

= (10 – 0.2) (10 + 0.2)

= (10)² - (0.2)²

= 100 – 0.04

= 90.96