Question

va rog!
descompuneti in factori,aplicand formula a^2-b^2=(a+b)(a-b)
a)4(2x-1)^2-25
b)x^2-4(x-3)^2
c)9x^2-(3x+4)^2

Answer 1

Răspuns:

Explicație pas cu pas:

a)

4(2x-1)^2 - 25 =

2^2(2x -1)^2 - 5^2 =

(4x -2 - 5)(4x - 2 + 5) =

(4x - 7)(4x + 3)

b)

x^2-4(x-3)^2 =

x^2 - 2^2(x-3)^2 =

(x - 2x + 6)(x + 2x - 6) =

(6 -x)(3x - 6)

c)

9x^2-(3x+4)^2  =

(3x)^2 - (3x + 4)^2 =

(3x - 3x - 4)(3x + 3x + 4) =

-4(6x + 4)

Answer 2

$\it a)\ 4(2x-1)^2-25=2^2(2x-1)^2-5^2=[2(2x-1)]^2-5^2=(4x-2)^2-5^2 =\\ \\ =(4x-2-5)(4x-2+5)=(4x-7)(4x+3)$

$\it x^2-4(x-3)^2=x^2-2^2(x-3)^2=x^2-[2(x-3)]^2=x^2-(2x-6)^2=\\ \\ = (x-2x+6)(x+2x-6)=(-x+6)(3x-6)= 3(-x+6)(x-2)=\\ \\ =-3(x-6)(x-2)$