Question

初二数学：因式分解

(1) 9(a-b)²+12(a²-b²)+4(a+b)²
(2) (x²-2x)²+2x²-4x+1
(3) 49(x-y)²-25(x+y)²
亲。最近极限赶作业。脑细胞死的惨。麻烦给出答案吧。

Answer 1

(1) 9(a-b)²+12(a²-b²)+4(a+b)²
= 9(a-b)²+12(a-b)(a+b)+4(a+b)²
=[3(a-b)+2(a+b)]^2
=(5a-b)^2

(2) (x²-2x)²+2x²-4x+1
=(x²-2x)²+2(x²-2x)+1
=(x^2-2x+1)^2
=(x-1)^4

(3) 49(x-y)²-25(x+y)²
=[7(x-y)+5(x+y)][7(x-y)-5(x+y)]
=(12x-2y)(2x-12y)
=4(6x-y)(x-6y)
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Answer 2

9(a-b)²+12(a²-b²)+4(a+b)²
完全平方式
=(3a-3b+2a+2b)^2
=（5a-b）^2

(x²-2x)²+2x²-4x+1
=(x²-2x)²+2(x²-2x)+1
完全平方式
=(x^2-2x+1)^2
=(x-1)^4

49(x-y)²-25(x+y)²
=（7x-7y+5x+5y）(7x-7y-5x-5y)
=(12x-2y)(2x-12y)
=4(6x-y)(x-6y)

Answer 3

解：
(1) 9(a-b)²+12(a²-b²)+4(a+b)²
=[2(a-b)]²+2×[2(a-b)]×[2(a+b)]+[2(a+b)]²
=[2(a-b)+2(a+b)]²
=(4a)²
=16a²
(2) (x²-2x)²+2x²-4x+1
=(x²-2x)²+2(x²-2x)+1
=(x²-2x+1)²
=(x-1)^4
(3) 49(x-y)²-25(x+y)²
=[7(x-y)+5(x+y)][7(x-y)-5(x+y)]
=(12x-2y)(2x-12y)
=4(6x-y)(x-6y)
]

Answer 4

9(a-b)²+12(a²-b²)+4(a+b)²
=9a²-18ab+9b²+12a²-12b²++4a²+8ab+4b²
=25a²-10ab+b²
=(5a-b)²

(x²-2x)²+2x²-4x+1
=(x²-2x)²+2(x²-2x)+1
=(x²-2x+1)²

49(x-y)²-25(x+y)²
=[7(x-y)+5(x+y)]*[7(x-y)-5(x+y)]
=(12x-2y)(2x-12y)
=4(6x-y)(x-6y)

Answer 5

（1）9（a²-2ab+b²）+12(a²-b²)+4(a²+2ab+b²)
=25a²-10ab+b²
=(5a-b)²
(2)(x²-2x)²+2(x²-2x)+1
=(x²-2x+1)²=(x-1)^4
(3)( 7(x-y)-5(x+y) ) ( 7(x-y)+5(x+y) )=(2x-12y)(12x-2y)=4(x-6y)(6x-y)