Question

因式分解 要过程 要快啊！！！！！！高悬赏啊分啊啊！！！

⑴y^2+4y-5
⑵y^4-26y^2+25
⑶(a-b)^2+6(b-a)+5
⑷2x^2-5x-12
⑸3x^2-5x-2
⑹6x^2-12xy+6y^2
⑺8x^2×y^2+6xy-35
⑻4a^2+4a-4a^2×b+b+1
⑼ax+16ay^2-a-8axy
⑽a(a^2-a-1)+1
⑾ab(m^2+n^2)+mn(a^2+b^2)

12、已知x-2y=-2b=-4 098，求2bx^2-8bxy+8by^2-8b的值
第六题错了
应该是6x^2-13xy+6y^2

Answer 1

第九题应为【ax^2+16ay^2-a-8axy】

⑴y^2+4y-5
=(y+5)(y-1)

⑵y^4-26y^2+25
=(y^2-1)(y^2-25)
=(y+1)(y-1)(y+5)(y-5)

⑶(a-b)^2+6(b-a)+5
=(a-b)^2-6(a-b)+5
=(a-b-1)(a-b-5)

⑷2x^2-5x-12
=(2x+3)(x-4)

⑸3x^2-5x-2
=(3x+1)(x-2)

⑹6x^2-12xy+6y^2
=6(x^2-2xy+y^2)
=6(x-y)^2

⑺8x^2×y^2+6xy-35
=(2xy+5)(4xy-7)

⑻4a^2+4a-4a^2×b+b+1
=4a^2+4a-4a^2×b+b+1

⑼ax^2+16ay^2-a-8axy
=a(x^2+16y^2-1-8xy)
=a(x^2-8xy+16y^2-1)
=a{(x-4y)^2-1}
=a(x-4y+1)(x-4y-1)

⑽a(a^2-a-1)+1
=a^3-a^2-a+1
=(a^3-a)-(a^2-1)
=a(a^2-1)-(a^2-1)
=(a^2-1)(a-1)
=(a+1)9a-1)(a-1)
=(a+1)(a-1)^2

⑾ab(m^2+n^2)+mn(a^2+b^2)
=abm^2+abn^2+a^2mn+b^2mn
=(abm^2+a^2mn) + (abn^2+b^2mn)
=am(bm+an) + bn(an+bm)
=(an+bm)(am+bn)

12、已知x-2y=-2b=-4 098，求2bx^2-8bxy+8by^2-8b的值
2bx^2-8bxy+8by^2-8b
=2b(x^2-4xy+4y^2-4)
=2b{(x-2y)^2 - 2^2}
=2b(x-2y+2)(x-2y- 2)
=4098 * (4098+2)(4098-2)
=4098*4100*4096
=68820172800

【问题补充：第六题错了应该是6x^2-13xy+6y^2】
6x^2-13xy+6y^2
= (2x-3y)(3x-2y)

Answer 2

y^2+4y-5=y²+5y-y-5=(y-1)(y+5)
y^4-26y^2+25=y^4-25y^-y^2+25=(y²-1)(y²-25)=(y+1)(y-1)(y-5)(y+5)
(a-b)^2+6(b-a)+5=(a-b)^2-5(a-b)-(a-b)+5=(a-b-1)(a-b-5)
2x^2-5x-12=2x²+3x-8x-12=x(2x+3)-8x-12=(2x+3)(x-4)
3x^2-5x-2=3x²-6x+x-2=(3x+1)(x-2)
6x^2-12xy+6y^2=6(x²-2xy+y²)=6(x-y)²
8x^2×y^2+6xy-35==(2xy+5)(4xy-7) 本题可以用十字相乘法...
4a^2+4a-4a^2×b+b+1=4a²+4a+1+b(1-4a²)=(2a+1)²+(1-2a)(1+2a)b=(2a+1)(2a+1-b+2ab)
ax²+16ay^2-a-8axy=a(x²+16y²-1-8xy)=a((x-4y)²-1)=a(x-4y+1)(x-4y-1)
a(a^2-a-1)+1=a³-a²-a+1=(a²-1)(a-1)=(a+1)(a-1)²
ab(m^2+n^2)+mn(a^2+b^2)=abm²+mna²+abn²+mnb²=am(bm+an)+bn(bm+an)=(am+bn)(bm+an)
2bx^2-8bxy+8by^2-8b=2b(x²-4xy+4y²)-4*2b=2b(x-2y)²-4*2b=2b[(x-2y)²-4]=2b(x-2y+2)(x-2y-2)
=4098*(-4098+2)(-4098-2)
=4098*4096*4100
=68820172800
呵呵，已经比较仔细了...
好好看，分解因式最好学会十字相乘法，很有用的..

追问

我一朋友也叫我用十字相乘法，可我们老师没说，根本不会啊

Answer 3

⑴y^2+4y-5=（y+5)(y-1)
⑵y^4-26y^2+25=(y^2-1)(y^2-25)=(y+1)(y-1)(y+5)(y-5)
⑶(a-b)^2+6(b-a)+5=(a-b-1)(a-b-5)
⑷2x^2-5x-12=(2x+3)(x-4)
⑸3x^2-5x-2=(3x+1)(x-2)
⑹6x^2-12xy+6y^2=6(x-y)^2
⑺8x^2×y^2+6xy-35=(2xy-5)(4xy+7)
⑻4a^2+4a^2×b+b+1=4a^2(b+1)+b+1=(4a^2+1)(b+1)
⑼ax+16ay^2-a-8axy=a(x+16y^2-1-8xy)
⑽a(a^2-a-1)+1=a(a^2-a)-a+1=a^2(a-1)-(a-1)=(a-1)(a^2-1)=(a-1)^2(a+1)
⑾ab(m^2+n^2)+mn(a^2+b^2)=abm^2+mna^2+abn^2+mnb^2
=am(an+bm)+bn(an+bm)
=(an+bm)(am+bn)
12、已知x-2y=-2b=-4 098，
2bx^2-8bxy+8by^2-8b=2b(x^2-4xy+4y^2-4b)=2b[(x-2y)^2-4b]=2b(b^2-4b)=2b^2(b-4)
=2*(-4098)^2*（4098-4）=137506029552

Answer 4

⑴y^2+4y-5
=(y+5)(y-1)
⑵y^4-26y^2+25
=(y²-25)(y²-1)
⑶(a-b)^2+6(b-a)+5
=(a-b)²-6(a-b)+5
=(a-b-1)(a-b-5)
⑷2x^2-5x-12
=(2x+3)(x-4)
⑸3x^2-5x-2
=(3x+1)(x-2)
⑹6x^2-12xy+6y^2
=6(x-y)²
⑻4a^2+4a-4a^2×b+b+1
=4a(a+b+1)+(b+1）
⑼ax+16ay^2-a-8axy
=a(x+y²-1-8xy)
=a(x-1)+y(y-8x）
12、已知x-2y=-2b=-4 098，求2bx^2-8bxy+8by^2-8b的值
2bx^2-8bxy+8by^2-8b
=2bx²-8bxy+8by²-8b
=2b(x²-4xy+4y²-4)
=(4098)[(x-2y)²-4]
=(4098)[(-4098)²-4]
=(-4098)³-4×(4098)

⑽a(a^2-a-1)+1
⑾ab(m^2+n^2)+mn(a^2+b^2)

12、已知x-2y=-2b=-4 098，求2bx^2-8bxy+8by^2-8b的值

Answer 5

1，(y+5)(y-1)
2,(y-25)(y-1)
3,(a-b-5)(a-b-1)
4,(2x+3)(x-4)
5,(3x+1)(x-2)
6,6(x+y)^2
我尽力咯，只写到这咯，用十字相乘法就可以咯，