Trova appunti, tesi, riassunti e versioni

Svolgimento: x^2-6x+9-y^2=(x-3)^2-y^2=((x-3)+y)((x-3)-y) .

Svolgimento: 4x^2-4x(2x-y+1)+(2x-y+1)^2=(2x-(2x-y+1))^2=(1-y)^2 .

Svolgimento: (x+3y)^2-(x+3y)(2x+5y)+1/4(2x+5y)^2=((x+3y)-(1/2(2x+5y)))^2=(3y-5/2y)^2=1/4y^2 .

Svolgimento: (2a-b)^2-2(2a-b)(a+2b)+(a+2b)^2=((2a-b)+(a+2b))^2=(3a+b)^2 .

Svolgimento: 18x^2+4xy+2/9y^2=2(9x^2+2xy+1/9y^2)=2(3x+1/3y)^2 .

Svolgimento: Essendo (a+b)^2-c^2=(a+b-c)(a+b+c) , si ha (2a-3)^2-16b^2=(2a-3+4b)(2a-3-4b) .

Svolgimento: (36)/(125)x^2-5/4y^2=1/5((36)/(25)x^2-(25)/4y^2)=1/5(6/5x+5/2y)(6/5x-5/2y) .

Svolgimento: (25)/2a^3-2a=1/2a(25a^2-4)=1/2a(5a-2)(5a+2) .

Svolgimento: 4x^3-xy^2=x(4x^2-y^2)=x(2x-y)(2x+y) .

Svolgimento: Essendo a^2-b^2=(a+b)(a-b) , si ha 81x^4-1/(16)y^8=(9x^2+1/4y^4)(9x^2-1/4y^4) .

Svolgimento: 2a^2x+2a^2y-2a^2-6abx-6aby+6ab=2a^2(x+y-1)-6ab(x+y-1)= =(2a^2-6ab)(x+y-1)=2a(a-3b)(x+y-1) .

Svolgimento: 6ax-3bx-4ay+2by-10a+5b=2a(3x-2y-5)-b(3x-2y-5)=(2a-b)(3x-2y-5) .

Svolgimento: 20ax-20bx+3ay-3by+5a-5b=a(20x+3y+5)-b(20x+3y+5)=(a-b)(20x+3y+5) .

Svolgimento: 2xy+3y-2x-3=2x(y-1)+3(y-1)=(2x+3)(y-1) .

Svolgimento: 10a^2b^2+20ab^3-2a^2b-4ab^2=10ab^2(a+2b)-2ab(a+2b)=(10ab^2-2ab)(a+2b)=2ab(5b-1)(a+2b) .

Svolgimento: 6a^2x-12abx-3a^2+6ab=3a^2(2x-1)-6ab(2x-1)=(3a^2-6ab)(2x-1)=3a(a-2b)(2x-1) .

Svolgimento: 3a^2-2ab-3a+2b=3a(a-1)-2b(a-1)=(3a-2b)(a-1) .

Svolgimento: 15a^3+10a^2b-9a-6b=5a^2(3a+2b)-3(3a+2b)= =(5a^2-3)(3a+2b)=(sqrt5a+sqrt3)(sqrt5a-sqrt3)(3a+2b) .

Svolgimento: 15x-6y-10x^2+4xy=3(5x-2y)-2x(5x-2y)=(3-2x)(5x-2y) .

Svolgimento: 3x-3y+x^2-xy=3(x-y)+x(x-y)=(3+x)(x-y) .