Evaluate: 103×107
Evaluate : 95× 96
Evaluate : 104×96
Answers
Answer:
(a) 11,021
(b) 9,120
(c) 9,984
Step-by-step explanation:
(a) 103 × 107
It can be written as ;
( 100 + 3 ) ( 100 + 7 )
Now, using identity :
( x + a ) ( x + b ) = x² + x ( a + b ) + ab
⇒ ( 100 + 3 ) ( 100 + 7 )
⇒ (100)² + 100 (3 + 7) + 3 * 7
⇒ 10000 + 300 + 700 + 21
⇒ 11, 021
_______________________
(b) 95 × 96
It can be written as ;
( 100 - 5 ) ( 100 - 4 )
Now, using identity :
( x - a ) ( x - b ) = x² - x ( a + b ) + ab
⇒ ( 100 - 5 ) ( 100 - 4 )
⇒ (100)² - 100 ( 5 + 4 ) + 5 * 4
⇒ 10000 - 500 - 400 + 20
⇒ 10000 - 900 + 20
⇒ 9100 + 20
⇒ 9,120
_______________________
(c) 104 × 96
It can be written as ;
( 100 + 4 ) ( 100 - 4 )
Now, using identity :
( a + b ) ( a - b ) = a² - b²
⇒ ( 100 + 4 ) ( 100 - 4 )
⇒ (100)² - (4)²
⇒ 10000 - 16
⇒ 9,984
_______________________
Answer:
(a) 11,021
(b) 9,120
(c) 9,984
Step-by-step explanation:
(a) 103 × 107
It can be written as ;
( 100 + 3 ) ( 100 + 7 )
Now, using identity :
( x + a ) ( x + b ) = x² + x ( a + b ) + ab
⇒ ( 100 + 3 ) ( 100 + 7 )
⇒ (100)² + 100 (3 + 7) + 3 * 7
⇒ 10000 + 300 + 700 + 21
⇒ 11, 021
_______________________
(b) 95 × 96
It can be written as ;
( 100 - 5 ) ( 100 - 4 )
Now, using identity :
( x - a ) ( x - b ) = x² - x ( a + b ) + ab
⇒ ( 100 - 5 ) ( 100 - 4 )
⇒ (100)² - 100 ( 5 + 4 ) + 5 * 4
⇒ 10000 - 500 - 400 + 20
⇒ 10000 - 900 + 20
⇒ 9100 + 20
⇒ 9,120
_______________________
(c) 104 × 96
It can be written as ;
( 100 + 4 ) ( 100 - 4 )
Now, using identity :
( a + b ) ( a - b ) = a² - b²
⇒ ( 100 + 4 ) ( 100 - 4 )
⇒ (100)² - (4)²
⇒ 10000 - 16
⇒ 9,984
_______________________