Question

29. Use (a + b)2 = a + 2ab + b2 to evaluate the following:
(a) (3.001) (b) (5.99) (c) 1001 x 999 (d) 5.63 x 5.63 +11.26 x 2.37 +2.37 x 2.37
(e) 8.79 x 8.79-8.79x 3.58 +1.79x 1.79​

Answer 1

we have to evaluate the following

(a) (3.001)² (b) (5.99)² (c) 1001 × 999

(d) 5.63 × 5.63 + 11.26 × 2.37 + 2.37 × 2.37

(e) 8.79 × 8.79 - 8.79 × 3.58 + 1.79 × 1.79

solution : (a) (3.001)²

= (3 + 0.001)²

using (a + b)² = a² + 2ab + b²

= 3² + 2(3)(0.001) + (0.001)²

= 9 + 0.006 + 0.000001

= 9.006001

(b) (5.99)²

= (6 - 0.01)²

using formula, (a - b)² = a² - 2ab + b²

= (6)² - 2(6)(0.01) + (0.01)²

= 36 - 0.12 + 0.0001

= 36.1201

(c) 1001 × 999

= (1000 + 1)(1000 - 1)

using formula, (a + b)(a - b) = a² - b²

= (1000)² - 1²

= 1000000 - 1

= 999999

(d) 5.63 × 5.63 + 11.26 × 2.37 + 2.37 × 2.37

= (5.63)² + 2(5.63)(2.37) + (2.37)²

now using formula, a² + 2ab + b² = (a + b)²

= (5.63 + 2.37)²

= 8²

= 64

(e) 8.79 × 8.79 - 8.79 × 3.58 + 1.79 × 1.79

= (8.79)² - 8.79 × 2(1.79) + (1.79)²

= (8.79)² - 2 × 8.79 × 1.79 + (1.79)²

using formula, a² - 2ab + b² = (a - b)²

= (8.79 - 1.79)²

= 7²

= 49