Question

silplify the following without multiplying:
​

Answer 1

Answer

1

Answer:

i)103-107

\boxed{\underline {Method 1}}

Method1

(100 + 3) (100 + 7)

Now, by using identity (x + a) (x + b) = x² + (a+b)*x + ab So,

x = 100, a = 3, b = 7

= (100)² + (3+7)*100 + (3*7)

= 10000 + 1000 + 21

=

11021\bf{(ii) 95 \times 96}(ii)95-96 \boxed{\underline {Method 1}}

Method1

(90 + 5) (90 + 6)

by using identity (x + a) (x + b) = x² + (a+b)*x + ab So,

x = 90, a = 5, b = 6

= (90)² + (5+6)*90 + (5*6)

= 8100 + 990 + 30

= 912010000 + 1000 + 21

= 11021

\boxed{\underline {Method 2}}

Method2

(110 - 7) (110 - 3)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100, a = (-7), b = (-3)

= (110)² + { (-7) + (-3) }*110 + {(-7)*(-3)}

= 12100 + (-10)*110 + 21

= 21200 - 1100 + 21

= 11021\bf{(iii) 104 \times 96}(iii)104x96 \boxed{\underline {Method 1}}

Method1

(100 + 4) (100 - 4)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab So,

x = 100, a = 4, b = (-4)

= (100)² + { 4 + (-4) }*100 + 4*(-4)

= 10000 + (4-4)*100 - 16

= 10000+ 0*100 - 16

= 10000 - 16\boxed{\underline {Method 2}}

Method2

(1005) (1004)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100, a = (-5), b = (-4)

= (100)² + { (-5) + (-4) }*100 + 20

= 10000 + (-9)*100 + 20

= 10000 - 9000 + 20

= 10020 - 900

= 9120

Answer 2

Solution:

(a) 109 × 50

= (1.09×10²) × (5×10)

= 1.09 × 5 × 10²+¹

= 1.09 × 5 × 10³

(b) 65 × 102

= (6.5×10) × (1.02×10²)

= 6.5 × 1.02 × 10¹+²

= 6.5 × 1.02 × 10³

(c) 102 ×21

= (1.02×10²) × (2.1×10)

= 1.02 × 2.1 × 10²+¹

= 1.02 × 2.1 × 10³

(d) 191 + 200 + 109

= 391 + 109

= 500

(e) 20 × 155

= (2×10) × (1.55×10²)

= 2 × 1.55 × 10¹+²

= 2 × 1.55 × 10³