十字相乘法:
1 x2-2x-35
=(x+5)(x-7)
2 x2+11x+10
=(x+1)(x+10)
3 a2-4a-21
=(a-7)(a+3)
4 m2-10mn+9n2
=(m-n)(m-9n)
5 2x2+5x+2
=(x+2)(2x+1)
6 3x2+x-2
=(x+1)(3x-2)
7 t2-7t+6
=(t-1)(t-6)
8 a2b2-4ab-5
=(ab)2-4ab-5
=(ab+1)(ab+5)
9 x2+8x+15
=(x+3)(x+5)
10 x2+2x-15
=(x-3)(x+5)
分组分解法:
1 4x2-a2-6a-9
=4x2-(a2+6a+9)
=4a2-(a+3)2
=(2x+a+3)(2x-a-3)
2 x2-y2+ax+ay
=(x+y)(x-y)+a(x+y)
=(x-y+a)(x+y)
3 p-q+k(p-q)
=(1+k)(p-q)
4 a2+2ab-ac-2ab
=(a2+2ab)-(ac+2bc)
=a(a+2b)-c(a+2b)
=(a-c)(a+2b)
5 5m(m-n)+5n(n-m)
=5m(m-n)-5n(m-n)
=(5m-5n)(m-n)
=5(m-n)2
6 a2-b2-c2+2bc
=a2-(b-c)2
=(a+b-c)(a-b+c)
7 m2+4n+4m+n2+4mn
=m2+n2+2mn+4m+4n
=(m+n)2+(4m+4n)
=(m+n)2+4(m+n)
=(m+n+4)(m+n)
8 16-a2-2ab-b2
=16-(a2+2ab+b2)
=16-(a+b)2
=(4+a+b)(4-a-b)
9 x2-4y2+4y-1
=x2-(4y2-4y+1)
=x2-(2y-1)2
=(x+2y-1)(x-2y+1)
10 ab+a+b+1
=(ab+a)+(b+1)
=a(a+b)+(b+1)
=(a+1)(b+1) 十字相乘法:
1 x2-2x-35
=(x+5)(x-7)
2 x2+11x+10
=(x+1)(x+10)
3 a2-4a-21
=(a-7)(a+3)
4 m2-10mn+9n2
=(m-n)(m-9n)
5 2x2+5x+2
=(x+2)(2x+1)
6 3x2+x-2
=(x+1)(3x-2)
7 t2-7t+6
=(t-1)(t-6)
8 a2b2-4ab-5
=(ab)2-4ab-5
=(ab+1)(ab+5)
9 x2+8x+15
=(x+3)(x+5)
10 x2+2x-15
=(x-3)(x+5)
分组分解法:
1 4x2-a2-6a-9
=4x2-(a2+6a+9)
=4a2-(a+3)2
=(2x+a+3)(2x-a-3)
2 x2-y2+ax+ay
=(x+y)(x-y)+a(x+y)
=(x-y+a)(x+y)
3 p-q+k(p-q)
=(1+k)(p-q)
4 a2+2ab-ac-2ab
=(a2+2ab)-(ac+2bc)
=a(a+2b)-c(a+2b)
=(a-c)(a+2b)
5 5m(m-n)+5n(n-m)
=5m(m-n)-5n(m-n)
=(5m-5n)(m-n)
=5(m-n)2
6 a2-b2-c2+2bc
=a2-(b-c)2
=(a+b-c)(a-b+c)
7 m2+4n+4m+n2+4mn
=m2+n2+2mn+4m+4n
=(m+n)2+(4m+4n)
=(m+n)2+4(m+n)
=(m+n+4)(m+n)
8 16-a2-2ab-b2
=16-(a2+2ab+b2)
=16-(a+b)2
=(4+a+b)(4-a-b)
9 x2-4y2+4y-1
=x2-(4y2-4y+1)
=x2-(2y-1)2
=(x+2y-1)(x-2y+1)
10 ab+a+b+1
=(ab+a)+(b+1)
=a(a+b)+(b+1)
=(a+1)(b+1)