Question

Разложить на множители 1)a^2+a 2)a^3+a^2 3)a^2+4a+4 4)b^2-25 5)4p^2-2p+1 6)8p^3+1 7)9x^2-6x+1 8)9x^2-1

Answer 1

1) а² + а= а(а +1)
2) а³+ а²=  а²(а +1)
3)а²+ 4а+ 4= (а+ 2)²
4)b²- 25= (b- 5)(b+ 5)
5)4p² - 2p+ 1= 2p( 2p- 1) + 1 
6) 8p³+ 1= (2p+ 1)(4p² - 2p+ 1)
7) 9x²- 6x+ 1= (3x -1)²
8)9x²- 1=  (3x-1)(3x+ 1)

Answer 2

1) a^2 + a can be factored as a(a+1). 2) a^3 + a^2 can be factored as a^2(a+1). 3) a^2 + 4a + 4 can be factored as (a+2)(a+2) or (a+2)^2. 4) b^2 - 25 can be factored as (b+5)(b-5). 5) 4p^2 - 2p + 1 cannot be factored further. 6) 8p^3 + 1 cannot be factored further. 7) 9x^2 - 6x + 1 can be factored as (3x-1)(3x-1) or (3x-1)^2. 8) 9x^2 - 1 can be factored as (3x+1)(3x-1).