Question

Exercitiul 10.Dau 50 puncte

Answer 1

[tex]10.\\\\ a)9y^2-(x^2-8x+16)=9y^2-(x-4)^2=\\ (aplicam~ a^2-b^2=(a-b)(a+b) ) \\ =(3y-x+4)(3y+x-4)\\\\ b)(x^2-2x+1) - 4y^2 =(x-1)^2 - (2y)^2=\\ =(x-1-2y)(x-1+2y) \\\\ c) 9y^2 - (x^2-8x+16) = (3y)^2 - (x-4)^2=\\ =(3y-x+4)(3y+x-4)\\\\ [/tex]
[tex]\\\\ d) 36 x^2+12x+1-49y^2 = (6x+1)^2-49y^2\\=(6x+1+7y)(6x+1-7y)\\\\ e)x^2-12x+36-y^2-8y-16 = (x-6)^2-(y+4)^2\\ =(x-6-y-4)(x-6+y+4)=(x-10-y)(x+2+y)\\\\ f) x^2+14xy+49y^2-a^2-6ab-9b^2 = (x+7y)^2-(a+3b)^2\\=(x+7y-a-3b)(x+7y+a+3b) \\\\ g)(9x^2-6x+1)-(4x^2+12x+9) = (3x-1)^2-(2x+3)^2\\=(3x-1-2x-3)(3x-1+2x+3)=(x-4)(5x+2)\\\\ g) (16x^2+8x+1)-(9x^2-12x+4)=(4x+1)^2-(3x-2)^2\\=(4x+1-3x+2)(4x+1+3x-2)
=(x+3)(7x-1)[/tex]

Answer 2

10)a) (x²+6x+9)-(y²-4y+4)=
=(x+3)²-(y-2)²=
=(x+3-y+2)(x+3+y-2)=
=(x+5-y)(x+1+y)
b) (x²-2x+1)-4y²=
=(x-1)²-(2y)²=
=(x-1+2y)(x-1-2y)
c)9y²-(x²-8x+16)=
=(3y)²-(x-4)²=
=(3y-x+4)(3y+x-4)
d)36x²+12x+1-49y²=
=(6x)²+12x+1-(7y)²=
=(6x+1)²-(7y)²=
=(6x+1-7y)(6x+1+7y)
e)x²-12x+36-y²-8y-16=
=(x-6)²-(y+4)²=
=(x-6-y-4)(x-6+y+4)=
=(x-10-y)(x-2+y)
f)x²+14xy+49y²-a²-6ab-9b²=
=(x+7y)²-(a+3b)²=
=(x+7y-a-3b)(x+7y+a+3b)
g)(9x²-6x+1)-(4x²+12x+9)=
=(3x-1)²-(2x+3)²=
=(3x-1-2x-3)(3x-1+2x+3)=
=(x-4)(5x+2)
h)(16x²+8x+1)-(9x²-12x+4)=
=(4x+1)²-(3x-2)²
=(4x+1-3x+2)(4x+1+3x-2)=
=(x+3)(7x-1)
Sper ca te-am ajutat !