Math(因式分解)

1.(3x-2)^3 - 8(x+1)^6
=(3x-2)^3 - [2(x+1)^2]^3
=[3x-2-2(x+1)^2][(3x-2)^2+(3x-2)(2(x+1)^2)+(2(x+1)^2)^2]
=(3x-2-2x^2 - 4x-2)[9x^2-12x+4+(3x-2)(2x^2+4x+2)+4(x^2+2x+1)^2]
=-(2x^2+x+4)(9x^2-12x+4+6x^3+8x^2-2x-4+4x^4+16x^3+24x^2+16x+4)
=-(2x^2+x+4)(4x^4+22x^3+41x^2+2x+4)

2.(a^2 -2ab+b^2)-25
=(a+b)^2-5^2
=(a+b+5)(a+b-5)

3.(x+2)^2 -(x+2)(y-3)- 6(y-3)^2
=[x+2-3(y-3)][x+2+2(y-3)]
=(x+2-3y+9)(x+2+2y-6)
=(x-3y+11)(x+2y-4)

1.(3x-2)³-8(x+1)³

=(3x-2)³-8(x+1)³

=(3x-2)³-(2³)(x+1)³

=(3x-2)³-(2(x+1))³----------拼合

=(3x-2)³-(2x+2)³------------拼合

=[(3x-2)-(2x+2)][(3x-2)²+(3x-2)(2x+2)+(2x+2)²]----套用恆等式a³-b³≡(a-b)(a²+ab+b²)

=(x)(9x²-4+6x²+6x-4x-4+4x²+4)

=x(19x²+2x-4)-------------------------------------------------答案

2.(a²-2ab+b²)-25

=(a+b)²-5²-------------------------------------------------------套用恆等式:a²-2ab+b²≡(a+b)²

=(a+b+5)(a+b-5)----------------------------------------------套用恆等式:a²+b²≡(a+b)(a-b)


3.(x+2)²-(x+2)(y-3)-6(y-3)²

=[x+2-3(y-3)][x+2+2(y-3)]---------------------------------抽(x+2-3(y-3))

=(y-3)(x+2-3)(x+2+2)---------------------------------------抽(y-3)

=(y-3)(x-1)(x+5)----------------------------------------------答案

1.(3x-2)^3 - 8(x+1)^6

=(3x-2)^3 - [2(x+1)^2]^3

=[3x-2-2(x+1)^2][(3x-2)^2+(3x-2)(2(x+1)^2)+(2(x+1)^2)^2]

=(3x-2-2x^2 - 4x-2)[9x^2-12x+4+(3x-2)(2x^2+4x+2)+4(x^2+2x+1)^2]

=-(2x^2+x+4)(9x^2-12x+4+6x^3+8x^2-2x-4+4x^4+16x^3+24x^2+16x+4)

=-(2x^2+x+4)(4x^4+22x^3+41x^2+2x+4)


2.(a^2 -2ab+b^2)-25

=(a+b)^2-5^2

=(a+b+5)(a+b-5)


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

=[x+2-3(y-3)][x+2+2(y-3)]

=(x+2-3y+9)(x+2+2y-6)

=(x-3y+11)(x+2y-4)