分解因式(數學)

1.(4a+b)(3a-2b)-2a(4a+b)

= (4a+b)(3a - b - 2a)

= (4a+b)(a-b)2.(a-b)(x-y)-(b-a)(x+y)

= (a-b)(x-y)+(a-b)(x+y)

= (a-b)(x-y+x+y)

= 2x(a-b)3.ab(a-b)^2+a(b-a)^2

= a(b+1)(a-b)^24.25(x+y)^2-16(x-y)^2

= [5(x+y)]^2 - [4(x-y)]^2

= [5(x+y)+4(x-y)][5(x+y)-4(x-y)]

= (9x+y)(x+9y)5.(a+b+c)^2-(a-b-c)^2

= (a+b+c+a-b-c)(a+b+c-a+b+c)

= 2a(2b+2c)

= 4a(b+c)6.x^3-64x

= x(x^2 - 64)

= x(x+8)(x-8)

1.
(4a+b)(3a-2b)-2a(4a+b)
=(4a+b)[(3a-2b)-2a]
=(4a+b)(a-2b)

2.
(a-b)(x-y)-(b-a)(x+y)
=(a-b)(x-y)+(a-b)(x+y)
=(a-b)[(x-y)+(x+y)]
=(a-b)(2x)

3.
ab(a-b)^2+a(b-a)^2
=ab(a-b)^2-a(a-b)^2
=(a-b)^2(ab+a)
=a(b+1)(a-b)^2

4.
25(x+y)^2-16(x-y)^2
=[5(x+y)-4(x-y)][5(x+y)+4(x-y)]
=(x+5y)(9x-y)

5.
(a+b+c)^2-(a-b-c)^2
=[(a+b+c)-(a-b-c)][(a+b+c)+(a-b-c)]
=(2b+2c)(2a)
=4a(b+c)

6.
x^3-64x
=x(x^2-64)
=x(x-8)(x+8)

1.(4a+b)(3a-2b)-2a(4a+b)
= (4a+b)(3a-2b-2a)
= (4a+b)(a-2b)

2.(a-b)(x-y)-(b-a)(x+y)
= (a-b)(x-y)+(a-b)(x+y)
= (a-b)(x-y+x+y)
= 2x(a-b)

3.ab(a-b)^2+a(b-a)^2
= (ab+a)(a+b)^2
= a(b+1)(a+b)^2

4.25(x+y)^2-16(x-y)^2
= (5x+5y)^2 - (4x-4y)^2
= (5x+5y+4x-4y)(5x+5y-4x+4y)
= (9x+y)(x+9y)

5.(a+b+c)^2-(a-b-c)^2
= (a+b+c+a-b-c)(a+b+c-a+b+c)
= 2a(2b+2c)
= 4a(b+c)

6.x^3-64x
= x(x^2 - 8^2)
= x(x+8)(x-8)