4條中二數學題。

1)
3(a+3b)^2 - 12(3a+b)^2
= -9(a+3b)^2
2)
4x^2 - 9y^2 - 2x - 3y
=2x(2x-1)-3y(3y+1)

3)
9x^2- y^2 + (3x+y)^2
= (3x-y)(3x+y)+(3x+y)^2
= (3x-y)(3x-y+3x+y)
=6x(3x-y)

1)
3(a+3b)^2-12(3a+b)^2
=3[(a^2)+(6ab)+(3b)^2]-12[(3a)^2+(6ab)+(b^2)]
=3(a^2+6ab+9b^2)-12(9a^2+6ab+b^2)
=(3a^2+18ab+27b^2)-(108a^2+72ab+12b^2)
=3a^2+18ab+27b^2-108a^2-72ab-12b^2
=3a^2-108a^2+18ab-72ab+27b^2-12b^2
=-105a^2-54ab+15b^2
=-3(7a+5b)(5a-b)
2)
4x^2-9y^2-2x-3y
=(2x)^2-(3y)^2-2x-3y
=(2x+3y)(2x-3y)-(2x+3y)
=(2x+3y)(2x-3y-1)
3)
9x^2-y^2+(3x+y)^2
=(3x)^2-y^2+(3x+y)^2
=(3x+y)(3x-y)+(3x+y)^2
=(3x+y)[(3x-y)+(3x+y)]
=(3x+y)(3x-y+3x+y)
=(3x+y)(3x+3x-y+y)
=6x(3x+y)
4)
4a^4-64b^4
=(2a^2)^2-(8b^2)^2
=(2a^2+8b^2)(2a^2-8b^2)
=2(a^2+4b^2)2(a^2-4b^2)
=4(a^2+4b^2)(a^2-4b^2)
=4(a^2+4b^2)[a^2-(2b)^2]
=4(a^2+4b^2)(a+2b)(a-2b)

1)
3(a+3b)^2-12(3a+b)^2
=3[(a^2)+(6ab)+(3b)^2]-12[(3a)^2+(6ab)+(b^2)]
=3(a^2+6ab+9b^2)-12(9a^2+6ab+b^2)
=(3a^2+18ab+27b^2)-(108a^2+72ab+12b^2)
=3a^2+18ab+27b^2-108a^2-72ab-12b^2
=3a^2-108a^2+18ab-72ab+27b^2-12b^2
=-105a^2-54ab+15b^2
=-3(7a+5b)(5a-b)
2)
4x^2-9y^2-2x-3y
=(2x)^2-(3y)^2-2x-3y
=(2x+3y)(2x-3y)-(2x+3y)
=(2x+3y)(2x-3y-1)
3)
9x^2-y^2+(3x+y)^2
=(3x)^2-y^2+(3x+y)^2
=(3x+y)(3x-y)+(3x+y)^2
=(3x+y)[(3x-y)+(3x+y)]
=(3x+y)(3x-y+3x+y)
=(3x+y)(3x+3x-y+y)
=6x(3x+y)
4)
4a^4-64b^4
=(2a^2)^2-(8b^2)^2
=(2a^2+8b^2)(2a^2-8b^2)
=2(a^2+4b^2)2(a^2-4b^2)
=4(a^2+4b^2)(a^2-4b^2)
=4(a^2+4b^2)[a^2-(2b)^2]
=4(a^2+4b^2)(a+2b)(a-2b)

1. 3(a+3b)^2 - 12(3a+b)^2
=3((a+3b)^2-(2(3a+b)^2)
=3(a+3b+6a+2b)(a+3b-6a-2b)
=3(7a+5b)(b-5a)

2. 4x^2 - 9y^2 - 2x -3y
= (2x+3y)(2x-3y)-(2x+3Y)
= (2x+3y)(2x-3y-1)

3. 9x^2 - y^2 + (3x+y)^2
= (3x+y)(3x-y) + (3x+y)^2
= (3x+y)(3x-y+3x+y)
= (3x+y)6x

4. 4a^4 - 64b^4
= 4((a^2)^2 -(4b^2)^2)
= 4(a^2+4b^2)(a^2-4b^2)
= 4(a^2+4b^2)(a+2b)(a-2b)