6條f.2因式分解(factorization) 急!!

Factorize the following by grouping terms.

1) x^2-9x+14

= x^2 - 7x - 2x + (7)(2)

= x ( x - 7 ) - ( 2x - 2(7) )

= x ( x - 7 ) - 2 ( x - 7 )

= ( x - 2 ) ( x - 7 )

2) 5x^2+8x-4

= 5x^2 - 2x + 10x - (2)(2)

= x ( 5x - 2 ) + 2 (5x) + 2 (-2)

= x ( 5x - 2 ) - 2 ( 5x - 2 )

= ( x - 2 ) ( 5x - 2 )

Without using a calculator, find the values of the following.

** a^2 - b^2 = ( a + b ) ( a - b ) **

1) 999^2-1

= 999^2 - 1^2

= ( 999 + 1 ) ( 999 - 1 )

= ( 1000 ) ( 998 )

= 998000

2) 1115^2-115^2

= ( 1115 + 115 ) ( 1115 - 115 )

= ( 1230 ) ( 1000 )

= 1230000

3) 4(19)^2-39^2

= ( 2^2 ) ( 19^2 ) - 39^2

= [ (2)(19) ] ^2 - 39^2

= 38^2 - 39^2

= ( 38 + 39 ) ( 38 - 39 )

= ( 77 ) ( -1 )

= -77

4) 2(75)^2-2(25)^2

= 2 ( 75^2 - 25^2 )

= 2 [ ( 75 + 25 ) ( 75 - 25 ) ]

= 2 [ ( 100 ) ( 50 ) ]

= 2 ( 5000 )

= 10000

Factorize the following by grouping terms.
1) (x-2)(x-7)
2) (5x-2)(x+2)

Without using a calculator, find the values of the following.
1) 999^2-1
= (999+1)(999-1)
= 1000(998)
= 998000

2) 1115^2 - 115^2
= (1115+115)(1115-115)
= 1230x1000
=1230000

3) 4(19)^2-39^2
= 1444-39^2
= 38^2-39^2
= (38+39)(38-39)
= 77(-1)
= -77

4) 2(75)^2-2(25)^2
= 11250-1250
= 10000