F.2 數學題目 因式分解

ac + 2ad - bc - 2bd
= a (c+2d) - b(c+2d)
= (a-b)(c+2d)

4x^2-12xy+9y^2
= (2x)^2-2*2x*3y+(3y)^2
= (2x - 3y)^2

44x^2 - 220xy+275y^2
= 11(4x^2-20xy+25y^2)
= 11((2x)^2-2*2x*5y+(5y)^2)
= 11(2x-5y)^2

(4x+2)(3y-z)+(3x-4)(z-3y)
= (4x+2)(3y-z)-(3x-4)(3y-z)
= [(4x+2)-(3x-4)](3y-z)
= (x+6)(3y-z)

5a^2c-(a-b)^2-5abc
= 5ac(a-b)-(a-b)^2
= (5ac-(a-b))(a-b)
- (5ac-a+b)(a-b)

(5x+y)^2-4(3x-2y)^2
=[(5x+y)-2(3x-2y)][(5x+y)+2(3x-2y)]
=(5y-x)(11x-3y)

2a^4-32
= 2((a^2)^2-4^2)
= 2(a^2-4)(a^2+4)
= 2(a-2)(a+2)(a^2+4)

ac+2ab-bc-2bd
=a(c+2b)-b(c+2d)
=(c+2d)(a-b)

4x^2-12xy+9y^2
=(2x-3y)(2x-3y)
=(2x-3y)^2



(4x+2)(3y-z)+(3x-4)(z-3y)
=(4x+2+3x-4)(z-3y)
=(7x-2)(z-3y)

2a''-32
=2a^4-2^5
=2(a^2-4)(a^2+4)

(5x+y)'-4(3x-2y)'
=25x^2+10xy+y^2-4(9x-12xy+4y^2)
=25x^2+10xy+y^2-38x^2+48xy-16y^2
=-13x^2+58xy-15y^2