Question

初中数学分解因式

1.7x²-63
2.a(x-y)+b(y-x)
3.x²-14+49
4.－4a²x+12ax-9x
5.－24x³+12x²-28x
6.(2x+y)²-(x+2y)²
要过程

Answer 1

1
7x^2-63
=7(x+3)(x-3)

2)
a(x-y)+b(y-x)
=(x-y)(a-b)

3)
x^2-14x+49
=(x-7)^2

4)-4a^2x+12ax-9x
=-x(4a^2-12a+9)
=-x(2a-3)^2

5)
-24x^3+12x^2-28x
=-4x(6x^2-3x+7)

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

Answer 2

很简单的题目，有打字的时间都做出来了，何必。

ps：第三题少了x。

Answer 3

1.原式=7(x²-9)=7(x-3)(x+3)
2.原式=ax-ay+by-bx=(a-b)x-(a-b)y=(a-b)(x-y)
3.原式=(x-7)²
4.原式=(-2ax-3)(2ax+3)[用十字交叉法]
5.原式=-4x（6x²-3x+7）
6.原式=4X²+4xy+y²-x²-4xy-4y²=3x²-3y²=3(x-y)(x+y)

Answer 4

1.7x²-63
=7(x²-9)
=7(x+3)(x-3)

2.a(x-y)+b(y-x)
=a(x-y)-b(x-y)
=(a-b)(x-y)

3.x²-14+49
=x²-2*7+7*7
=(x-7)²

4.－4a²x+12ax-9x
=-x(4a²-12a+9)
=-x(2*2a²-2*2*3a+3*3)
=-x(2a-3)²

5.－24x³+12x²-28x
=-4x(6x²-3x+7)

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