Question

please answer mathematics questions​

Answer 1

Question:

Simplify the following using suitable formulae:

2) ( 128 )² - ( 77 )²

3) ( 467 )² - ( 33 )²

4) ( 79 )² - ( 69 )²

5) 197 × 203

6) 113 × 87

Answer:

2) ( 128 )² - ( 77 )² = 10455

3) ( 467 )² - ( 33 )² = 217000

4) ( 79 )² - ( 69 )² = 1480

5) 197 × 203 = 39991

6) 113 × 87 = 9831

Step-by-step-explanation:

2) ( 128 )² - ( 77 )²

→ ( 128 + 77 ) ( 128 - 77 ) - - [ a² - b² = ( a + b ) ( a - b ) ]

→ ( 205 ) ( 51 )

→ 205 × 51

→ 10455

$\rule{200}{1}$

3) ( 467 )² - ( 33 )²

→ ( 467 + 33 ) ( 467 - 33 ) - - [ a² - b² = ( a + b ) ( a - b ) ]

→ ( 500 ) ( 434 )

→ 500 × 434

→ 217000

$\rule{200}{1}$

4) ( 79 )² - ( 69 )²

→ ( 79 + 69 ) ( 79 - 69 ) - - [ a² - b² = ( a + b ) ( a - b ) ]

→ ( 148 ) ( 10 )

→ 148 × 10

→ 1480

$\rule{200}{1}$

5) 197 × 203

→ ( 200 - 3 ) ( 200 + 3 )

→ ( 200 )² - ( 3 )² - - [ ( a + b ) ( a - b ) = a² - b² ]

→ 40000 - 9

→ 39991

$\rule{200}{1}$

6) 113 × 87

→ ( 100 + 13 ) ( 100 - 13 )

→ ( 100 )² - ( 13 )² - - [ ( a + b ) ( a - b ) = a² - b² ]

→ 10000 - 169

→ 9831