幫我計幾條數學題(20點)

1.
左方=(-x+4)(5-x)(5x-2)
=(-5x+x2+20-4x)(5x-2)
=(x2-9x+20)(5x-2)
=5x3-45x2+100x-2x2+18x-40
=5x3-47x2+118x-40
比較左方和右方同類項,可得
A=5,B=47,C=-118,D=-40

2.
左方=A(2x2+3x-5)-B(x-2)
=2Ax2+3Ax-5A-Bx+2B
=2Ax2+(3A-B)x+(2B-5A)
比較左方和右方同類項,可得
2A=8
A=4

3A-B=5
12-B=5
B=7


3.
左方=A(4x2+7)-B(6x+4)+C
=4Ax2+7A-6Bx-4B+C
=4Ax2-6Bx+(7A-4B+C)
比較左方和右方同類項,可得
4A=8
A=2

6B=18
B=3

7A-4B+C=3
14-12+C=3
C=1


4. 2Ax2-B(-3x+2)2+Cx=44x2-47x+16(計A,B,C,恆等式)
左方=2Ax2-B(-3x+2)2+Cx
=2Ax2-(9Bx2-12Bx+4B)+Cx
=(2A-9B)x2+(12B+C)x-4B
比較左方和右方同類項,可得

2A-9B=44________________(1)
12B+C=-47_______________(2)
-4B=16___________________(3)
解(1),(2)和(3),可得
A=4,B=-4,C=1

5. (x+3)2-2x-6
=x2+6x+9-2x-6
=x2+4x+3
=(x+1)(x+3)


6. (2x-5)(x-3)+(3x-1)(5-2x)
=(2x-5)(x-3)-(3x-1)(2x-5)
=(2x-5)[(x-3)-(3x-1)]
=(2x-5)(-2x-2)
=-2(2x-5)(x+1)

7. (x+3)2-16
=[(x+3)+4}[(x+3)-4}
=(x+7)(x-1)


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

=[(x+1)+(2x-1)][(x+1)-(2x-1)]
=3x(-x+2)
=3x(2-x)