关于因式分解(1)48x²+22x-15(2)21x²+31x-42(3)35x²+23x-6(4)(x+y)²-5(x²-y²)+6(x-y)²(5)4x²-14xy+6y²-7x+y-2这五道题我绞尽脑汁也想不出,用提公因式法、公式法、十字相乘法来解,其他的我还没学到、我初二.

问题描述:

关于因式分解
(1)48x²+22x-15
(2)21x²+31x-42
(3)35x²+23x-6
(4)(x+y)²-5(x²-y²)+6(x-y)²
(5)4x²-14xy+6y²-7x+y-2
这五道题我绞尽脑汁也想不出,用提公因式法、公式法、十字相乘法来解,其他的我还没学到、我初二.


(1)48x²+22x-15=(8x-3)(6x+5)
(2)21x²+31x-42=(7x-6)(3x+7)
(3)35x²+23x-6=(5x-1)(7x+6)
(4)(x+y)²-5(x²-y²)+6(x-y)²=[(x+y-2(x-y)][(x+y)-3(x-y)]=(3y-x)(4y-2x)=2(3y-x)(2y-x)
(5)4x²-14xy+6y²-7x+y-2=(4x-2y)(x-3y)-7x+y-2=(4x-2y+1)(x-3y-2)

1.=(x+1+√841)(x+1-√841)这是根据二元一次方程的求根公式得出的
对于方程ax2+bx+c=0的两个解 x=(-b±√b2-4ac)/2a
4.=2(x-2y)(x-3y)

(1)48x²+22x-15 =(8x+5)(6x-3)
(2)21x²+31x-42=(7x+14)(3x-3)
(3)35x²+23x-6=(7x+6)(5x-1)
(4)(x+y)²-5(x²-y²)+6(x-y)²=(x+y)²-5(x+y)(x-y)+6(x-y)²=[(x+y)+(x-y)][(x+y)-6(x-y)]
= -2x(5x-7y)
(5)4x²-14xy+6y²-7x+y-2=4x²-(14xy+7x)+(6y²+y-2)=4x²-x(14y+7)+(2y-i)(3y+2)
=[x-(3y+2)][4x-(2y-1)]=(x-3y-2)(4x-2y+1)

1)
48x²+22x-15
十字相乘法:
8 -3
6 5
48x²+22x-15
=(8x-3)(6x+5)
(2)
21x²+31x-42
十字相乘法:
3 7
7 -6
21x²+31x-42
=(3x+7)(7x-6)
(3)35x²+23x-6
十字相乘法:
5 -1
7 6
35x²+23x-6
=(5x-1)(7x+6)
(4)(x+y)²-5(x²-y²)+6(x-y)²
十字相乘法:
x+y -2(x-y)
x+y -3(x-y)
(x+y)²-5(x²-y²)+6(x-y)²
=[(x+y)-2(x-y)][(x+y)-3(x-y)]
=(-x+3y)(-2x+4y)
=2(x-3y)(x-2y)
(5)4x²-14xy+6y²-7x+y-2
=(x-3y)(4x-2y)-7x+y-2
=(x-3y)(4x-2y)+(x-3y)-8x+4y-2
=(x-3y)(4x-2y+1)-2(4x-2y+1)
=(4x-2y+1)(x-3y-2)

(1)48x²+22x-15原式=(8x-3)(6x+5)利用十字相乘:如下8 -36 5(2)21x²+31x-42原式=(7x-6)(3x+7)7 -63 7(3)35x²+23x-6原式=(7x+6)(5x-1)7 65 -1(4)(x+y)²-5(x²-y²)+6...