Giúp mình với! Bài 7: Phân tích thành nhân tử ( Nhóm hạng tử),$1)~ax^2-3axy+bx-3by$ $2)~5x^2y+5xy^2-a^2x-a^2y$,$3)~2ax^3+6ax^2+6ax+18a$ $4)~10xy^2-5by^2+2ax-ab$,$5)~ax-bx+cx-3a+3b-3c$ $6)~2ax-bx+3cx-2a+b-3c$,$7)~ax-bx-2cx-2a+2b+4c$ $8)~3ax^2+3bx^2+ax+bx+5a+5b$,$9)~ax^2-bx^2-2ax+2bx-3a+3b$

Question

Accepted Answer

Bài 7: Phân tích thành nhân tử (Nhóm hạng tử)

1) ax2−3axy+bx−3by

ax2−3axy+bx−3by=(ax2−3axy)+(bx−3by)=ax(x−3y)+b(x−3y)=(x−3y)(ax+b)

2) 5x2y+5xy2−a2x−a2y

5x2y+5xy2−a2x−a2y=(5x2y+5xy2)−(a2x+a2y)=5xy(x+y)−a2(x+y)=(x+y)(5xy−a2)

3) 2ax3+6ax2+6ax+18a

2ax3+6ax2+6ax+18a=2a(x3+3x2+3x+9)=2a[(x3+3x2)+(3x+9)]=2a[x2(x+3)+3(x+3)]=2a(x+3)(x2+3)

4) 10xy2−5by2+2ax−ab

10xy2−5by2+2ax−ab=(10xy2−5by2)+(2ax−ab)=5y2(2x−b)+a(2x−b)=(2x−b)(5y2+a)

5) ax−bx+cx−3a+3b−3c

ax−bx+cx−3a+3b−3c=(ax−bx+cx)−(3a−3b+3c)=x(a−b+c)−3(a−b+c)=(a−b+c)(x−3)

6) 2ax−bx+3cx−2a+b−3c

2ax−bx+3cx−2a+b−3c=(2ax−bx+3cx)−(2a−b+3c)=x(2a−b+3c)−1(2a−b+3c)=(2a−b+3c)(x−1)

7) ax−bx−2cx−2a+2b+4c

ax−bx−2cx−2a+2b+4c=(ax−bx−2cx)−(2a−2b−4c)=x(a−b−2c)−2(a−b−2c)=(a−b−2c)(x−2)

8) 3ax2+3bx2+ax+bx+5a+5b

3ax2+3bx2+ax+bx+5a+5b=(3ax2+3bx2)+(ax+bx)+(5a+5b)=3x2(a+b)+x(a+b)+5(a+b)=(a+b)(3x2+x+5)

9) ax2−bx2−2ax+2bx−3a+3b

ax2−bx2−2ax+2bx−3a+3b=(ax2−bx2)−(2ax−2bx)−(3a−3b)=x2(a−b)−2x(a−b)−3(a−b)=(a−b)(x2−2x−3)=(a−b)(x2−3x+x−3)=(a−b)[x(x−3)+1(x−3)]=(a−b)(x−3)(x+1)