⑴y^2+4y-5⑵y^4-26y^2+25⑶(a-b)^2+6(b-a)+5⑷2x^2-5x-12⑸3x^2-5x-2⑹6x^2-12xy+6y^2⑺8x^2×y^2+6xy-35⑻4a^2+4a-4a^2×b+b+1⑼ax+16ay^2-a-8axy⑽a(a^2-a-1)+1⑾ab(m^2+n^2)+mn(a^2+b^2)12、已知x-2y=-2b=-4098,求2bx^2-8bxy+8by^2-8b的值第六

Question

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)