因式分解問題 急

因式分解問題 急
1. －49+t^2
=t^2－7^2
=(t－7)(t+7)

2. 100e－1

3. 49f^2－g^2
=(7t)^2－g^2
=(7t－g)(7t+g)

4. 4r^2－25s^2
=(2r)^2－(5s)^2
=(2r－5s)(2r+5s)

5. 3(x+y)y+6(x+y)x
=(x+y)(3y)+(x+y)(6x)
=(6x+3y)(x+y)
=3(2x+y)(x+y)

6. 5ac+4c+15a－3b－bc+12
=(5ac+4c)+(15a+12)－(3b+bc)
=c(5a+4)+3(5a+4)－b(3+c)
=(c+3)(5a+4)－b(3+c)
=(5a－b+4)(c+3)

7. 6(a+1)^2－4(a+1)
=2(a+1)[3(a+1)－2]
=2(a+1)(3a+1)

8. 2x^2+2xy+3z+2xz+3y+3x
=(2x^2+2xy)+(3z+2xz)+(3y+3x)
=2x(x+y)+z(3+2x)+3(x+y)
=(2x+3)(x+y)+z(3+2x)
=(2x+3)(x+y+z)

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

1.
-49+t^2
=t^2-49
=(t-7)(t+7)

2.
100e^2-1
=(10e-1)(10e+1)

3.
49f^2-g^2
=(7f-g)(7f+g)

4
4r^2-25s^2
=(2r-5s)(2r+5s)

5
3(x+y)y+6(x+y)x
=3(x+y)(y+2x)

6
5ac+4c+15a-3b-bc+12
=5ac+4c+15a+12-3b-bc
=c(5a+4)+3(5a+4)-b(3+c)
=(5a+4)(c+3)-b(3+c)
=(5a+4-b)(c+3)

7
6(a+1)^2-4(a+1)
=2(a+1)[3(a+1)-2]
=2(a+1)(3a+3-2)
=2(a+1)(3a+1)

8
2x^2+2xy+3z+2xz+3y+3x
=2x(x+y)+z(3+2x)+3(y+x)
=(x+y)(2x+3)+z(2x+3)
=(x+y+z)(2x+3)

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