[中二]因式分解4題

3y^4 - 6y^2 + 3 = 3(y^4 - 2y^2 +1)
= 3(y^2 - 1)^2
= 3 (y+1)^2 (y-1)^2
4a^2 - 4ab^2 + b^4 - c^2 = (4a^2 - 4ab^2 + b^4) - c^2
= (2a - b^2)^2 - c^2
= (2a - b^2 + c)(2a - b^2 -c)
25a^2 - 10a + 1 -16b^2 + 24b - 9 = (25a^2 - 10a + 1) - (16b^2 - 24b + 9)
= (5a - 1)^2 - (4b - 3)^2
= [(5a-1)+(4b-3)][(5a-1)-(4b-3)]
= (5a+4b-4)(5a-4b+2)
2x(a-3b) - y(3b-a) + 4x(a+3b) + 2y(3b+a) = 2x(a-3b) + y(a-3b) + 4x(a+3b) + 2y(3b+a)
= (2x+y)(a-3b) + 2(2x)(a+3b)+2(y)(a+3b)
= (2x+y)(a-3b) +2(a+3b)(2x+y)
= (2x+y)[a-3b+2(a+3b)]
= (2x+y)(a-3b+2a+6b)
= (2x+y)(3a+3b)
= 3(2x+y)(a+b)

2012-08-21 23:32:01 補充：
Note: Q4. - y(3b-a) = + y(a-3b)
because -(a-b) = b-a
你想factorisation(因式分解) 好啲,
一定要努力背同靈活用identities
a^2 - b^2 = (a+b)(a-b)
(a+/-b)^2 = a^2 +/- 2ab +b^2

3y^4-6y^2+3
=3(y^4-2y^2+1)
=3(y^2-1)^2
=3(y+1)^2(y-1)^2

4a^2-4ab^2+b^4-c^2
=(4a^2-4ab^2+b^4)-c^2
=(2a-b^2)^2-c^2
=(2a-b^2+c)(2a-b^2-c)

25a^2-10a+1-16b^2+24b-9
=(25a^2-10a+1)-(16b^2-24b+9)
=(5a-1)^2-(4b-3)^2
=(5a-1+4b-3)(5a-1-4b+3)
=(5a+4b-4)(5a-4b+2)

2x(a-3b)-y(3b-a)+4x(a+3b)+2y(3b+a)
=2x(a-3b)+y(a-3b)+4x(a+3b)+2y(a+3b)
=(a-3b)(2x+y)+2(a+3b)(2x+y)
=(2x+y)(a-3b+2a+6b)
=(2x+y)(3a+3b)
=3(2x+y)(a+b)

3y^4 - 6y^2 + 3
=3(y^4-2y^2+1)
=3(y^2-1)^2
=3(y-1)^2(y+1)^2

4a^2 - 4ab^2 + b^4 - c^2
=(2a-b^2)^2-c^2
=[(2a-b^2)-c][(2a-b^2)+c]
=(2a-b^2-c)(2a-b^2+c)

25a^2 - 10a + 1 -16b^2 + 24b - 9
=(5a-1)^2-(4b-3)^2
=[(5a-1)-(4b-3)][(5a-1)+(4b-3)]
=(5a-4b+2)(5a+4b-4)

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