Question

Phân tích thành nhân tử(đầy đủ các bước)

a. (a+b)^2-4

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

c. 49a^2-(2a-b)^2

d. (4a+3b)^2-(b-2a)^2

e.9(a+b)^2-4(a-2b)^2

 

 

Answer 1

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

b: \(=\left(a-2b-2b\right)\left(a-2b+2b\right)=a\left(a-4b\right)\)

c: \(=\left(7a-2a+b\right)\left(7a+2a-b\right)\)

\(=\left(5a+b\right)\left(9a-b\right)\)

d: \(=\left(4a+3b-b+2a\right)\left(4a+3b+b-2a\right)\)

\(=\left(6a+2b\right)\left(2a+4b\right)\)

\(=4\left(3a+b\right)\left(a+2b\right)\)

e: \(=\left(3a+3b\right)^2-\left(2a-4b\right)^2\)

\(=\left(3a+3b-2a+4b\right)\left(3a+3b+2a-4b\right)\)

\(=\left(a+5b\right)\left(5a-b\right)\)

Answer 2

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

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

`c)49a^2-(2a-b)^2=(7a-2a+b)(7a+2a-b)=(5a+b)(9a-b)`

`d)(4a+3b)^2-(b-2a)^2=(4a+3b-b+2a)(4a+3b+b-2a)=(6a+2b)(2a+4b)`

`e)9(a+b)^2-4(a-2b)^2=[3(a+b)-2(a-2b)][3(a+b)+2(a-2b)]`

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

                               `=(a+7b)(5a-b)`

Answer 3

a) (a + b)² - 4

= (a + b)² - 2²

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

b) (a - 2b)² - 4b²

= (a - 2b)² - (2b)²

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

= (a - 4b).a

Answer 4

c) 49a² - (2a - b)²

= (7a)² - (2a - b)²

= [7a - (2a - b)][7a + (2a - b)]

= (5a + b)(9a - b)

d) (4a + 3b)² - (b - 2a)²

= [(4a + 3b) - (b - 2a)][(4a + 3b) + (b - 2a)]

=(6a + 2b)(2a + 4b)

= 4(3a + b)(a + 2b)

Answer 5

e) 9(a + b)² - 4(a - 2b)²

= [3(a + b)]² - [2(a - 2b)]²

= (3a + 3b)² - (2a - 4b)²

= [(3a + 3b) - (2a - 4b)][(3a + 3b) + (2a - 4b)]

= (a + 7b)(5a - b)