factorize the expressions

1. 25(3x - 2y)² – 9(2x + y)²
=25(9x²-12xy+4y²)-9(4x²+4xy+y²)
=225x²-300xy+100y²-36x²-36xy-9y²
=189x²-336xy+91y²
=(9x-13y)(21x-7y)

2. (a² + b²)² – 4a²b²
=(a² + b²)²–(2ab)².........4a²b²=2²a²b²=(2ab)²
=(a² + b²-2ab)(a² + b²+2ab)........用a²-b²=(a+b)(a-b)
=(a+b)²(a-b)²
=[(a+b)(a-b)]²......應該吳洗咁都得@.@

3. 12(c² + 2) – 2(c² + 2)² – 18
=-2[(c² + 2)² -6(c²+2)+9]...........抽公因數
=-2[(c² + 2)² -2(3)(c²+2)+3²]
=-2(c²+2-3)².................a²-2ab+b²=(a-b)²
=-2(c²-1)²
=-2(c²-1²)².......又有得a²-b²=(a+b)(a-b)
=-2[(c-1)(c+1)]²

4. (x² – x)² – 4(x² – x) - 12
=(x² – x)² – 2(2)(x² – x) +2² -16..............2²-16=-12
=(x²-x-2)²-16............用a²-2ab+b²=(a-b)²
=(x²-x-2)²-4²........a²-b²=(a+b)(a-b)
=(x²-x-2+4)(x²-x-2-4)
=(x²-x+2)(x²-x-6)..........x²-x-6 可以因式分解= =
=(x²-x+2)(x+2)(x-3)

Q1 : that is a common factor 7 !!
(21x-7y) = 7(3x-y)

1. 25(3x - 2y)2 – 9(2x + y)2

=[5(3x-2y)-3(2x+y)][5(3x-2y)+3(2x+y)]
=(15x-10y-6x-3y)(15x-10y+6x+3y)
=(9x-16y)(21x-7y)
2. (a2 + b2)2 – 4a2b2
=(a4 +2a2b2+ b4) – 4a2b2
=a4 -2a2b2+ b4
=(a2-b2)

3. 12(c2 + 2) – 2(c2 + 2)2 – 18
=2[6(c2 + 2) – (c2 + 2)2 – 9]
=2[6(c2 + 2) – (c2 + 2-3)(c2 + 2+3)]
=2[6(c2 + 2) – (c2 -1)(c2 + 5)]

4. (x2 – x)2 – 4(x2 – x) - 12
=[(x2 – x)-6][(x2 – x)+2]
=(x2 – x-6)(x2 – x+2)