因式分解(數學)

1.16a^4-b^4

= (2a)^4 - b^4

= [(2a)^2 - b^2][(2a)^2 + b^2]

= (2a-b)(2a+b)(4a^2+b^2)2.(x+y)^2+6z(x+y)+9z^2

= (x+y+3z)(x+y+3z)3.(m-n)^2-8m(m-n)+16m^2

= (m-n-4m)(m-n-4m)

= (3m+n)(3m+n)4.2ab-a^2-b^2

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

= -(a-b)(a-b)5.x^3+4x^2yz+4xy^2z

= x(x^2+4xyz+4y^2z)

= x(x+2yz)(x+2yz)6.(x^2+4)^2-16x^2

= (x^2+4+4x)(x^2+4-4x)

= (x+2)^2(x-2)^2

= (x^2-4)^213 (x/2 + 2y/3 -3z/4)^2 -(x/2-2y/3-3z/4)^2

= (x/2+2y/3-3z/4+x/2-2y/3-3z/4)(x/2+2y/3-3z/4-x/2+2y/3+3z/4)

= (x-6z/4)(4y/3)

1.
16a^4-b^4
=(4a^2+b^2)(4a^2-b^2)
=(2a-b)(2a+b)(4a^2+b^2)

2.
(x+y)^2+6z(x+y)+9z^2
=[(x+y)+3z]^2
=(x+y+3z)^2

3.
(m-n)^2-8m(m-n)+16m^2
=[(m-n)-4m]^2
=(3m-n)^2

4.
2ab-a^2-b^2
=-a^2+2ab-b^2
=-(a-2ab+b)^2
=-(a-b)^2

5.
x^3+4x^2yz+4xy^2z
=x(x^2+4xyz+4y^2z)
=x(x+2yz)^2

6.
(x^2+4)^2-16x^2
=[(x^2+4)-4x][(x^2+4)+4x]
=(x^2-4x+4)(x^2+4x+4)
=(x-2)^2(x+2)^2

13.
(x/2 + 2/3y -3/4z)^2 -(x/2-2/3y-3/4z)^2
=[(x/2 + 2/3y -3/4z )-(x/2-2/3y-3/4z) ][(x/2 + 2/3y -3/4z)+(x/2-2/3y-3/4z) ]
=(5x/2)(8y/3+11z/4)
=(5x/2)[(32y+32z)/12]