因式分解 f.2 maths

1.
5xy - 10xz² -12z² + 6y
= (5xy- 10xz²) + (6y - 12z²)
= 5x(y - 2z²) +6(y - 2z²)
= (5x + 6)(y - 2z²)


2.
14h² + 9k+ 18hk+ 7h
= (14h² + 7h) + (18hk + 9k)
= 7h(2h + 1) + 9k(2h + 1)
= (7h + 9k)(2h + 1)


3.
10abc + 5c - 5d - 10abd
= (10abc - 10abd) + (5c + 5d)
= 10ab(c - d) + 5(c - d)
= (10ab + 5)(c - d)
= 5(2ab + 1)(c - d)


4.
2rst + rs + 6tu + 3u
= (2rst+ rs) + (6tu + 3u)
= rs(2t + 1) + 3u(2t + 1)
= (rs + 3u)(2t + 1)


5.
a³ + a² + ab + b
= (a³ + a²) + (ab + b)
= a²(a + 1) + b(a + 1)
= (a² + b)(a + 1)


6.
6ax + 9bx + 8ay + 12by
= (6ax+ 9bx) + (8ay+ 12by)
= 3x(2a + 3b) + 4y(2a + 3b)
= (3x + 4y)(2a + 3b)


7.
10x³ - 10x² +5x - 5
= (10x³ - 10x²) + (5x- 5)
= 10x²(x- 1) + 5(x - 1)
= (10x² + 5)(x - 1)
= 5(2x² + 1)(x - 1)


8.
3x²y² - 3xy - 6xy + 6
= (3x²y² - 3xy) - (6xy - 6)
= 3xy(xy- 1) - 6(xy - 1)
= (3xy - 6)(xy - 1)
= 3(xy - 2)(xy - 1)


9.
ax + ay + az - bx - by - bz
= (ax+ ay+ az) - (bx + by+ bz)
= a(x + y + z) - b(x + y + z)
= (a - b)(x + y + z)


10.
am + 2bm - 3cm + 12cn- 4an - 8bn
= (am + 2bm - 3cm) - (4an + 8bn - 12cn)
= m(a + 2b - 3c) - 4n(a + 2b - 3c)
= (m - 4n)(a + 2b - 3c)


11.
a³ + a²b + a²c - ab² - b²c -b³
= (a³ + a²b + a²c) - (ab² + b³ + b²c)
= a²(a + b + c) - b²(a+ b + c)
= (a² - b²)(a+ b + c)
= (a - b)(a + b)(a + b + c)


12.
x²yz + x + xy²z + y + xyz² + z
= (x²yz + x)+ (xy²z + y) + (xyz² + z)
= x(xyz + 1) + y(xyz + 1) + z(xyz + 1)
= (x + y + z)(xyz + 1)

1.)
5xy -10xz^2 - 12z^2 +6y
=5x(y-2z^2)-6(2z^2-y)
=5x(y-2z^2)+6(y-2z^2)
=(y-2z^2)(5x+6)

2.)
14h^2 +9k +18hk +7h
=7h(2h+1)+9k(1+2h)
=(1+2h)(7h+9k)

3.)
10abc+5c-5d-10abd
=10ab(c-d)+5(c-d)
=5(c-d)(2ab+1)

4.)
2rst +rs +6tu+3u
=rs(2t+1)+3u(2t+1)
=(2t+1)(rs+3u)

5.)
a^3 +a^2 +ab +b
=a^2(a+1)+b(a+1)
=(a+1)(a^2+b)

6.)
6ax +9bx +8ay +12by
=3x(2a+3b)+4y(2a+3b)
=(2a+3b)(3x+4y)

7.)
10x^3 -10x^2 + 5x - 5
=10x^2(x-1)+5(x-1)
=5(x-1)(2x^2+1)

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

9.)
ax +ay +az - bx - by - bz
=a(x+y+z)-b(x+y+z)
=(x+y+z)(a-b)

10.)
am + 2bm - 3cm +12cn - 4an - 8bn
=m(a+2b-3c)-4n(-3c+a+2b)
=(a+2b-3c)(m-4n)

11.)
a ^3 + a^2 b +a ^2 c -ab^2 - b^2 c - b^3
=(a ^3 - b^3)+(a^2 b -ab^2 )+(a ^2 c - b^2 c)
=(a-b)(a^2+ab+b^2)+ab(a-b)+c(a+b)(a-b)
=(a-b)[(a^2+ab+b^2)+ab+c(a+b)]
=(a-b)[a^2+2ab+b^2+c(a+b)]
=(a-b)[(a+b)^2+c(a+b)]
=(a-b)(a+b)(a+b+c)

12.)
x^2 yz +x + xy ^2 z +y+xyz^2 +z
=(x+y+z)+(x^2 yz +xy ^2 z+xyz^2)
=(x+y+z)+xyz(x+y+z)
=(x+y+z)(1+xyz)

1.) (5x+6)(y-2z^2)
2.) (7h+9k)(1+2h)
3.) (5c-5d)(1+2ab)
4.) (rs+3u)(1+2t)
5.) (a+1)(a^2+b)
6.) (2a+3b)(3x+4y)
7.) (2x^2+1)(5x-5) or 5(2x^2+1)(x+1)
8.) (3xy-6)(xy-1) or 3(xy-1)(xy-2)
9.) (x+y+z)(a-b)
10.) (a+2b-3c)(m-4n)
11.) (a^2-b^2)(a+b+c)
12.) (x+y+z)(xyz+1)