數學題　　　　急急　　　　１０

1).

( a + b + 1 ) ( a + b + 1) ...... ( 1 )

代 x = a + b 入 ( 1 )

= ( x + 1 ) ( x + 1 )

= x^2 + 2x + 1...... ( 2 )

代 x = a + b 入 ( 2 )

= ( a + b )^2 + 2( a + b ) + 1
= a^2 + 2ab + b^2 + 2a + 2b + 1
= a^2 + b^2 + 2ab + 2a + 2b + 1


2).

( a + b + c + d ) ( a + b - c - d )

= ( a + b + c + d ) [ ( a + b ) - ( c + d ) ] ...... ( 1 )

代 a + b = x , c + d = y 入 ( 1 )

= ( x + y ) ( x - y )

= ( x^ 2 - y^ 2 ) ...... ( 2 )

代 x = a + b , y = c + d 入 ( 2 )

= ( a + b )^ 2 - ( c + d )^ 2
= a^2 + 2ab + b^2 - c^2 - 2cd - d^2


3).

( x^2 + x + 1 ) ( x^2 - x + 1) ..... ( 1 )

代 y = x^ 2 + 1 入 ( 1 )

= ( y + x ) ( y - x )

= y^2 - x^2 ..... ( 2 )

代 y = x^2 + 1 入 ( 2 )

= ( x^2 + 1 )^ 2 - x^2

= x^ 4 + 2x^2 + 1 - x^2

= x^4 + x^2 + 1

1) a^2 +2ab+b^2+2a+2b+1

2) a^2+2ab+b^2-c^2-2cd-d^2

3) x^4+x^2+1