1.(3x+5)(2x-3)=6x^2+x-15

1.
(3x+5)(2x-3)=6x^2+x-15
LHS
= (3x+5)(2x-3)
= 6x^2-9x+10x-15
= 6x^2+x-15
= RHS
therefore, (3x+5)(2x-3) 三 6x^2+x-15 (三 = 全等)



2.
找出未知數
(2x+1)(x-3)=Ax^2+Bx+C
LHS
= (2x+1)(x-3)
= 2x^2-6x+x-3
= 2x^2-5x-3
所以A = 2, B = -5, C = -3

(如果要用(1)答案做)
LHS
= [(3x+5)-(x+4)] [(2x-3)-x)]
= (3x+5)(x-3) - x(3x+5) - (x+4)(2x-3) + x(x+4)
= (3x+5)(x-3) - x(3x+5-x-4) - (2x^2-3x+8x-12)
= (3x+5)(x-3) - x(2x+1) - (2x^2+5x-12)
= 6x^2+x-15 - 2x^2-x - 2x^2-5x+12..........(把(1)答案套入)
= (6-2-2)x^2 + (1-1-5)x + (12-15)
= 2x^2+5x-3
所以A = 2, B = -5, C = -3

1.
(3x+5)(2x-3)=6x^2+x-15
6x^2-9x+10x-15=6x^2+x-15
6x^2+x-15=6x^2+x-15
0=0
it is an identity
2. (2x+1)(x-3)=2x^2-6x+x-3
=2x^2-5x+3
By comparing the like terms,
A=2 B=-5 C=3