These are all equations that can be solved by expanding and simplifying both sides of the equation:
1) (3х+5)(4х-1) = 12x^2 + 12x - 5(6х-3)(2х+7) = 12x^2 + 36x - 6
Since both sides of the equation simplify to the same expression (12x^2 + 12x - 5), the equation is true for all values of x.
2) (5х-1)(2-х) = 10 - 7x - x^2(х-3)(2-5х) = 10 - 7x - x^2
Since both sides of the equation simplify to the same expression (10 - 7x - x^2), the equation is true for all values of x.
3) (5х+1)(2х-3) = 10x^2 - 15x + 2x - 3(10х-3)(х+1) = 10x^2 + 10x - 3x - 3
Since both sides of the equation simplify to the same expression (10x^2 - 15x + 2x - 3), the equation is true for all values of x.
4) (7х-1)(х+5) = 7x^2 + 35x - x - 5(3+7х)(х+3) = 7x^2 + 21x + 3x + 9
These two sides do not simplify to the same expression, so this equation is not true for all values of x.
These are all equations that can be solved by expanding and simplifying both sides of the equation:
1) (3х+5)(4х-1) = 12x^2 + 12x - 5
(6х-3)(2х+7) = 12x^2 + 36x - 6
Since both sides of the equation simplify to the same expression (12x^2 + 12x - 5), the equation is true for all values of x.
2) (5х-1)(2-х) = 10 - 7x - x^2
(х-3)(2-5х) = 10 - 7x - x^2
Since both sides of the equation simplify to the same expression (10 - 7x - x^2), the equation is true for all values of x.
3) (5х+1)(2х-3) = 10x^2 - 15x + 2x - 3
(10х-3)(х+1) = 10x^2 + 10x - 3x - 3
Since both sides of the equation simplify to the same expression (10x^2 - 15x + 2x - 3), the equation is true for all values of x.
4) (7х-1)(х+5) = 7x^2 + 35x - x - 5
(3+7х)(х+3) = 7x^2 + 21x + 3x + 9
These two sides do not simplify to the same expression, so this equation is not true for all values of x.