Question

Using (x + a) (x + b) = x^2 + (a + b) x + ab, find (i) 103 × 104 (ii) 5.1 × 5.2 (iii) 103 × 98 (iv) 9.7 × 9.8

Answer 1

Solution:

Formula used:

$(x + a)(x + b) = {x}^{2} + (a + b)x + ab$
$1) \: 103 \times 104 \\ \\ here \: x = 100 \: \: a = 3 \: \: \: b = 4 \\ \\ = > (100 + 3) \times (100 + 4) \\ \\ = > ( {100)}^{2} + (3 + 4) \times 100 + 3 \times 4 \\ \\ = > 10000 + 7 \times 100 + 12 \\ \\ = > 10000 + 700 + 12 \\ \\ = > 10712$
$2) \: 5.1 \times 5.2 \\ \\ = > (5 + 0.1) \times (5 + 0.2) \\ \\ = > {(5)}^{2} + (0.1 + 0.2) \times 5 + 0.1 \times 0.2 \\ \\ = > 25 + 0.3 \times 5 + 0.02 \\ \\ = > 25 + 1.5 + 0.02 \\ \\ = > 26.52$
$3) \: 103 \times 98 \\ \\ = > (100 + 3) \times (100 - 2) \\ \\ = > ( {100)}^{2} + (3 - 2) \times 100 - 2 \times 3 \\ \\ = > 10000 + 100 - 6 \\ \\ = > 10100 - 6 \\ \\ = > 10094$
$4) \: 9.7 \times 9.8 \\ \\ = > (10 - 0.3) \times( 10 - 0.2) \\ \\ = > ( {10)}^{2} - (0.2 + 0.3)10 + 0.3 \times 0.2 \\ \\ = > 100 - 5 + 0.06 \\ \\ = > 100.06 - 5 \\ \\ = > 95.06$
Hope it helps you

Answer 2

Answer with Step-by-step explanation:

1) 103 x 104

= (100 + 3)(100 + 4)

By using the formula  ,(x + a) (x + b) = x²+ (a + b) x + ab    

= 100² + (3 + 4)100 + (3×4)

= 10000 + 700 + 12

= 10712

 

2) 5.1 x 5.2

= (5 + 0.1)(5 + 0.2)

By using the formula  ,(x + a) (x + b) = x²+ (a + b) x + ab  

= 5² + (0.1+0.2)5 + (0.1×0.2)

= 25 + 1.5 + 0.02

= 26.52

 

3) 103 x 98

= (100 + 3)(100 - 2)

By using the formula  ,(x + a) (x + b) = x²+ (a + b) x + ab  

= 100² + (3-2)100 – (3×2)

= 10000 + 100 - 6

= 10094

 

4) 9.7 x 9.8

= (9 + 0.7 )(9 + 0.8)

By using the formula  ,(x + a) (x + b) = x²+ (a + b) x + ab  

= 9² + (0.7 + 0.8)9 + (0.7×0.8)

= 81 + 13.5 + 0.56

= 95.06

HOPE THIS ANSWER WILL HELP YOU...

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