`a^2 + ab + 2a + 2b = a(a+2) + b(a+2) = (a+b)(a+2)`

Bài 1: 

a: \(4a^2-6b=2\left(2a^2-3b\right)\)

b: \(m^3n-2m^2n^2-mn\)

\(=mn\left(m^2-2mn-1\right)\)

Bài 1:

a) \(4a^2-6b=2\left(a^2-3b\right)\)

b) \(=mn\left(m^2-2mn-1\right)\)

Bài 2:

a) \(=4\left(u-2\right)^2+v\left(u-2\right)=\left(u-2\right)\left(4u-8+v\right)\)

b) \(=a\left(a-b\right)^3-b\left(a-b\right)^2-b^2\left(a-b\right)=\left(a-b\right)\left[a\left(a-b\right)^2-b\left(a-b\right)-b^2\right]=\left(a-b\right)\left(a^3-2a^2b+ab^2-ab+b^2-b^2\right)=\left(a-b\right)\left(a^3-2a^2b+ab^2-ab\right)\)

1A:

a: \(x^3+2x=x\left(x^2+2\right)\)

b: \(3x-6y=3\left(x-2y\right)\)

c: \(5\left(x+3y\right)-15x\left(x+3y\right)\)

\(=5\left(x+3y\right)\left(1-3x\right)\)

d: \(3\left(x-y\right)-5x\left(y-x\right)\)

\(=3\left(x-y\right)+5x\left(x-y\right)\)

\(=\left(x-y\right)\left(5x+3\right)\)

1A. a. x(x²+2) 

b. 3(x-2y)

c. 5(x+3y)(1-3x) 

d. (x-y) (3-5x)

1B. a. 2x(2x-3)

b.xy(x²-2xy+5)

c. 2x(x+1)(x+2)

d. 2x(y-1)+2y(y-1)=2(y-1)(x-y)

1B:

a: \(4x^2-6x=2x\left(2x-3\right)\)

b: \(x^3y-2x^2y^2+5xy\)

\(=xy\left(x^2-2xy+5\right)\)

a:=2(x-2)+y(x-2)

=(x-2)(y+2)

b: \(=\left(x+y\right)^2-4\)

=(x+y+2)(x+y-2)

`a, 9x^2 - 16 = (3x+4)(3x-4)`

`b, 4x^2 - 12xy + 9y^2 = (2x-3y)^2`

`c, t^3-8 = (t-2)(t^2 - 2t + 4)`

`d, 2ax^3y^3 + 2a = 2a(x^3y^3 + 1) = 2a(xy+1)(x^2y^2 - xy + 1)`

a) \(\left(9x^2-16\right)=\left(3x-4\right)\left(3x+4\right)\)

b) \(4x^2-12xy+9y^2=\left(2x-3y\right)^2\)

c) \(t^3-8=\left(t-2\right)\left(t^2+2t+4\right)\)

d) \(2ax^3y^3+2a=2a\left(x^3y^3+1\right)\)

a) \(4x^2-1=\left(2x+1\right)\left(2x-1\right)\)

b) \(\left(x+2\right)^2-9=\left(x-1\right)\left(x+5\right)\)

c) \(\left(a+b\right)^2-\left(a-2b\right)^2\)

\(=\left(a+b-a+2b\right)\left(a+b+a-2b\right)\)

\(=3b\left(2a-b\right)\)

`a, 4x^2-1 = (2x+1)(2x-1)`

`b, (x+2)^2-9 = (x+2-3)(x+2+3) = (x-1)(x+5)`

`c, (a+b)^2-(a-2b)^2 = (a+b+a-2b)(a+b-a+2b) = (2a-b)(3b)`

Câu 1:

a: Sửa đề: \(A=\left(x+2\right)\left(x^2-2x+4\right)+x\left(1-x\right)\left(1+x\right)\)

\(=x^3+2^3+x\left(1-x^2\right)\)

\(=x^3+8+x-x^3\)

=x+8

b: Khi x=-4 thì A=-4+8=4

c: Đặt A=-2

=>x+8=-2

=>x=-10

Câu 2:

a: \(x^3-3x^2=x^2\cdot x-x^2\cdot3=x^2\left(x-3\right)\)

b: \(5x^3+10x^2+5x\)

\(=5x\cdot x^2+5x\cdot2x+5x\cdot1\)

\(=5x\left(x^2+2x+1\right)\)

\(=5x\left(x+1\right)^2\)

\(a^2-6x-4b^2+9=\left(a-3\right)^2-4b^2\\ =\left(a-3-2b\right)\left(a-3+2b\right)\)

a) \(=x\left(x^2-2xy+y^2\right)=x\left(x-y\right)^2\)

b) \(=\left(x^2+2x\right)+\left(10x+20\right)=x\left(x+2\right)+10\left(x+2\right)=\left(x+2\right)\left(x+10\right)\)

c) đặt \(x^2+x+1=t\)

\(\left(x^2+x+1\right)\left(x^2+x+4\right)+2=t\left(t+3\right)+2=t^2+3t+2=\left(t^2+t\right)+\left(2t+2\right)=t\left(t+1\right)+2\left(t+1\right)=\left(t+1\right)\left(t+2\right)=\left(x^2+x+2\right)\left(x^2+x+3\right)\)