3條form 2 factorization (5點)

(1)及(2)都利用恒等式 a^2 - b^2 = (a - b)(a + b)
(1) 9(2a+b)^2-16(a-b)^2
= [3(2a+b)]^2 - [4(a-b)]^2
= [3(2a+b) + 4(a-b)][3(2a+b) - 4(a-b)]
= (6a+3b+4a-4b)(6a+3b-4a+4b)
= (10a-b)(2a+7b)
(2)1-(x-y)^4
= 1^2 - [(x-y)^2]^2
= [1 - (x-y)^2][1 + (x-y)^2]
= [1^2 - (x-y)^2][1 + x^2 - 2xy + y2^]
= [1 - (x-y)][1 + (x-y)](x^2 - 2xy + y^2 + 1)
= (1- x + y)(1 +x - y)(x^2 - 2xy + y^2 + 1)
(3)-8(m-n)^2+48(m-n)-72
= -8[(m-n)^2 - 6(m-n) + 9]
= -8[(m-n)^2 - 3(m-n) - 3(m-n) + 9]
= -8{(m-n)[(m-n) - 3] - 3[(m-n) - 3]}
= -8(m - n - 3)^2

1.) 9(2a+b)^2-16(a-b)^2
= [3(2a+b)^2]-[4(a-b)^2]
= (6a+3b)^2-(4a-4b)^2
= [6a+3b+(4a-4b)] [6a+3b-(4a-4b)]
= (6a+3b+4a-4b)(6a+3b-4a+4b)
= (10a-b)(2a+7b)

2009-12-31 14:13:20 補充：
2.)1-(x-y)^4
= 1^2- [(x-y)^2]^2
= [1-(x-y)^2][1+(x-y)^2]
= [1^2-(x-y)^2][1+x^2-2(x)(y)+y^2]
= [1-(x-y)][1+(x-y)](1+x^2-2xy+y^2)
= (1-x+y)(1+x-y) (1+x^2-2xy+y^2)

1. 9(2a+b)^2-16(a-b)^2

=3^2(2a+b)^2-4^2(a-b)^2

=(6a+3b)^2-(4a-4b)^2

=(6a+3b+4a-4b)(6a+3b-4a+4b)

=(10a-b)(2a+7b)



2. 不識DO

3. -8(m-n)^2+48(m-n)-72
=-8【(m-n)^2+6(m-n)-72】
=-8【(m+n)(m-n)+6(m-n)-72】
=-8【(m+n+6)(m-n)-72】
=-8(m^2-n^2+6m-6n-72)