Алгебра 7 класс, Дорофеев. №695 а) a(a+b)-b(a-b) б)2x(x-y)-y(y-2x) в)a(a^2 -1)+a^2(a-1)...

Question

Алгебра 7 класс, Дорофеев. №695
а) a(a+b)-b(a-b)
б)2x(x-y)-y(y-2x)
в)a(a^2 -1)+a^2(a-1)
г)4m(m-2)-(4m^2-8)
д)2(x^2-7)+(7-2x^2)
е)3x(x-y)+3y(x+y)

Answer 1

а) a(a+b)-b(a-b) = (a-b)(a+b)(a-b)
б)2x(x-y)-y(y-2x) = (2x-y)(x-y)(y-2x) = (y-x)(2x-y)(2x-y) = (y-x)(2x-y)²
в)a(a² -1)+a²(a-1) = (a+a²)(a-1)(a+1)(a-1) = a(1+a)(a-1)(a+1)(a-1) a(a²-1)²
г)4m(m-2)-(4m²-8) = 4m(m-2) - 4m(m-2) = 0
д)2(x²-7)+(7-2x²) = 2x² - 14 + 7 - 2x² = -7
е)3x(x-y)+3y(x+y) = 3x+3y (x-y)(x+y) = 3(x+y)(x-y)(x+y)