Question

因式分解：帮忙做一下 a^2+b^2-c^2-4d^2-2ab+4cd x^2+4y^2+9z^2-4xy-12xyz+6xz (x+2)(x-2)-4y(x-y)-5

Answer 1

a^2+b^2-c^2-4d^2-2ab+4cd
=(a^2-2ab+b^2)-(c^2-4cd+4d^2)
=(a-b)^2-(c-2d)^2
=(a-b+c-2d)(a-b-c+2d)

x^2+4y^2+9z^2-4xy-12yz+6xz
=x^2+(-2y)^2+(3z)^2+2x(-2y)+2(-2y)(3z)+2x(3z)
=(x-2y+3z)^2 (平方和公式，一步就可以得到了)

(x+2)(x-2)-4y(x-y)-5
=x^2-4-4xy+4y^2-5
=x^2-4xy+4y^2-9
=(x-2)^2-3^2
=(x-2+3)(x-2-3)
=(x+1)(x-5)

Answer 2

a^2+b^2-c^2-4d^2-2ab+4cd
=a^2+b^2-2ab-(c^2+4d^2-4cd)
=(a-b) ²-(c-2d)²
=(a-b-c+2d)(a-b+c-2d)

x^2+4y^2+9z^2-4xy-12yz+6xz
=x^2-4xy+4y^2+9z^2+6xz-12yz
=(x-2y)²+6z(x-2y)+9z²
=(x-2y+3z)²

(x+2)(x-2)-4y(x-y)-5
=x²-4-4xy+4y²-5
=x²-4xy+4y²-9
=(x-2y)²-3²
=(x-2y-3)（x-2y+3）