Đáp án:
$4)
a) (x-3)(x-4)\\
b) (x-1)(2x+1)(7+3x)\\
c) (2x+1)(8-2x)\\
d) (x-5).(-1)\\
e) (3x-2)(2x-6)\\
5)
a)(a-b)(2a-2b)\\
b) (xy-3)(5y^2-2z)\\
c) (2x-y)(4x+1)\\
d) abc^2(b-a)(b+c)\\
e) (y-z)(x-z)(x-y)$
Giải thích các bước giải:
$4)
a) (x-3)(x-1)-3(x-3)=(x-3)(x-1-3)=(x-3)(x-4)\\
b) (x-1)(2x+1)+3(x-1)(x+2)(2x+1)=(x-1)(2x+1)(1+3x+6)=(x-1)(2x+1)(7+3x)\\
c) (6x+3)-(2x-5)(2x+1)=3(2x+1)-(2x-5)(2x+1)=(2x+1)(3-2x+5)=(2x+1)(8-2x)\\
d) (x-5)^2+(x+5)(x-5)-(5-x)(2x+1)=(x-5)(x-5+x+5-2x-1)=(x-5).(-1)\\
e) (3x-2)(4x-3)-(2-3x)(x-1)-2(3x-2)(x+1)\\
=(3x-2)(4x-3)+(3x-2)(x-1)-2(3x-2)(x+1)\\
=(3x-2)(4x-3+x-1-2x-2)\\
=(3x-2)(2x-6)\\
5)
a) (a-b)(a+2b)-(b-a)(2a-b)-(a-b)(a+3b)\\
=(a-b)(a+2b)+(a-b)(2a-b)-(a-b)(a+3b)\\
=(a-b)(a+2b+2a-b-a-3b)\\
=(a-b)(2a-2b)\\
b) 5xy^3-2xyz-15y^2+6z\\
=(5xy^3-15y^2)+(6z-2xyz)\\
=5y^2(xy-3)+2z(3-xy)\\
=5y^2(xy-3)-2z(xy-3)\\
=(xy-3)(5y^2-2z)\\
c) (x+y)(2x-y)+(2x-y)(3x-y)-(y-2x)\\
=(x+y)(2x-y)+(2x-y)(3x-y)+(2x-y)\\
=(2x-y)(x+y+3x-y+1)\\
=(2x-y)(4x+1)\\
d) ab^3c^2-a^2b^2c^2+ab^2c^3-a^2bc^3\\
=abc(b^2c-abc+bc^2-ac^2)\\
=abc\left [ bc(b-a)+c^2(b-a) \right ]\\
=abc^2(b-a)(b+c)\\
e) x^2(y-z)+y^2(z-x)+z^2(x-y)\\
=x^2(y-z)+y^2(z-x)+z^2(x-y)\\
=x^2(y-z)+(y^2z-xy^2)+(xz^2-yz^2)\\
=x^2(y-z)+y^2z-xy^2+xz^2-yz^2\\
=x^2(y-z)+(y^2z-yz^2)+(xz^2-xy^2)\\
=x^2(y-z)+yz(y-z)-x(y^2-z^2)\\
=x^2(y-z)+yz(y-z)+x(y-z)(y+z)\\
=(y-z)(x^2+yz-xy-xz)\\
=(y-z)\left [ x(x-z)-y(x-z) \right ]\\
=(y-z)(x-z)(x-y)$
