Question

$\huge\sf{Quality \: answer \: needed}$

Evaluate the following products without multiplying directly :-

1. 103 x 107
2. 95 x 96
3. 104 x 96

Answer 1

${\large{\bf{\red{\underline{\underline{Given :}}}}}}$

Evaluate the following products without multiplying directly :-

1. 103 x 107

2. 95 x 96

3. 104 x 96

${\large{\bf{\orange{\underline{\underline{Solution :}}}}}}$

${\bf{1.103 \times 107}}$

${\mapsto{\sf{(100 + 3)(100 + 7)}}}$

${\mapsto{\sf{ {(100)}^{2} + (3 + 7)(100) + (3)(7)}}}$

${\mapsto{\sf{10000+1000+21}}}$

${\blue{\mapsto{\red{\boxed{\bf{11021}}}}}}$

${\bf{2.95 \times 96}}$

${\mapsto{\sf{(90+5)(90+6)}}}$

${\mapsto{\sf{ {(90)}^{2} +(5+6)(90)+(5)(6)}}}$

${\mapsto{\sf{8100+990+30}}}$

${\blue{\mapsto{\red{\boxed{\bf{9120}}}}}}$

${\bf{3.104 \times 96}}$

${\mapsto{\sf{(100+4)(100−4)}}}$

${\mapsto{\sf{ {(100)}^{2} − {(4)}^{2} }}}$

${\mapsto{\sf{10000−16}}}$

${\blue{\mapsto{\red{\boxed{\bf{9984}}}}}}$

￣￣￣￣￣￣￣￣￣￣￣￣

Answer 2

Step-by-step explanation:

Evaluate the following products without multiplying directly :-

1. 103 x 107

2. 95 x 96

3. 104 x 96

{\large{\bf{\orange{\underline{\underline{Solution :}}}}}}

Solution:

{\bf{1.103 \times 107}}1.103×107

{\mapsto{\sf{(100 + 3)(100 + 7)}}}↦(100+3)(100+7)

{\mapsto{\sf{ {(100)}^{2} + (3 + 7)(100) + (3)(7)}}}↦(100)

2

+(3+7)(100)+(3)(7)

{\mapsto{\sf{10000+1000+21}}}↦10000+1000+21

{\blue{\mapsto{\red{\boxed{\bf{11021}}}}}}↦

11021

{\bf{2.95 \times 96}}2.95×96

{\mapsto{\sf{(90+5)(90+6)}}}↦(90+5)(90+6)

{\mapsto{\sf{ {(90)}^{2} +(5+6)(90)+(5)(6)}}}↦(90)

2

+(5+6)(90)+(5)(6)

{\mapsto{\sf{8100+990+30}}}↦8100+990+30

{\blue{\mapsto{\red{\boxed{\bf{9120}}}}}}↦

9120

{\bf{3.104 \times 96}}3.104×96

{\mapsto{\sf{(100+4)(100−4)}}}↦(100+4)(100−4)

{\mapsto{\sf{ {(100)}^{2} − {(4)}^{2} }}}↦(100)

2

−(4)

2

{\mapsto{\sf{10000−16}}}↦10000−16

{\blue{\mapsto{\red{\boxed{\bf{9984}}}}}}↦

9984