Question

phân tích thành nhân tử 

1. (a+3b)^2-9b^2

2. 4a^2-(a+b)^2

3. x^3+3x^2+3x+1

Answer 1

1: =(a+3b+3b)(a+3b-3b)

=a(a+6b)

2: =(2a-a-b)(2a+a+b)=(a-b)(3a+b)

3: =(x+1)³

Answer 2

`1)(a+3b)^2-9b^2=(a+3b-3b)(a+3b+3b)=a(a+6b)`

`2)4a^2-(a+b)^2=(2a-a-b)(2a+a+b)=(a-b)(3a+b)`

`3)x^3+3x^2+3x+1=(x+1)^3`

Answer 3

\(1.\left(a+3b\right)^2-9b^2=\left(a+3b+9b\right)\left(a+3b-9b\right)=\left(a+12b\right)\left(a-6b\right)\)

\(2.4a^2-\left(a+b\right)^2=\left(2a+a+b\right)\left(2a-a-b\right)=\left(3a+b\right)\left(a-b\right)\)

\(3.x^3+3x^2+3x+1\)

\(=x^3+1+3x^2+3x\)

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

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

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

Answer 4

1.

\(\left(a+3b\right)^2-9b^2\)

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

\(=\left(a+3b\right).\left(a-3b\right)\)

\(=a\left(a+6\right)\)

2.

\(4a^2-\left(a+b\right)^2\)

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

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

\(=\left(a-b\right).\left(3a+b\right)\)

3.

\(x^3+3x^2+3x+1\)

\(=x^3+3.x^2.1+3.x.1^2+1^3\)

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