Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 486

а) $$\sqrt{x}$$($$\sqrt{a}$$ − $$\sqrt{b}$$) = $$\sqrt{x}$$ ⋅ $$\sqrt{a}$$ − $$\sqrt{x}$$ ⋅ $$\sqrt{b}$$ = $$\sqrt{ax}$$ − $$\sqrt{bx}$$
б) ($$\sqrt{x}$$ + $$\sqrt{y}$$)$$\sqrt{x}$$ = $$\sqrt{x}$$ ⋅ $$\sqrt{x}$$ + $$\sqrt{x}$$ ⋅ $$\sqrt{y}$$ = $$\sqrt{x²}$$ + $$\sqrt{xy}$$ = x + $$\sqrt{xy}$$
в) $$\sqrt{ab}$$($$\sqrt{a}$$ + $$\sqrt{b}$$) = $$\sqrt{ab}$$ ⋅ $$\sqrt{a}$$ + $$\sqrt{ab}$$ ⋅ $$\sqrt{b}$$ = $$\sqrt{a²b}$$ + $$\sqrt{ab²}$$ = a$$\sqrt{b}$$ + b$$\sqrt{a}$$
г) ($$\sqrt{m}$$ − $$\sqrt{n}$$)$$\sqrt{mn}$$ = $$\sqrt{m}$$ ⋅ $$\sqrt{mn}$$ − $$\sqrt{n}$$ ⋅ $$\sqrt{mn}$$ = $$\sqrt{m²n}$$ − $$\sqrt{mn²}$$ = m$$\sqrt{n}$$ − n$$\sqrt{m}$$
д) ($$\sqrt{x}$$ + $$\sqrt{y}$$)(2$$\sqrt{x}$$ − $$\sqrt{y}$$) = $$\sqrt{x}$$ ⋅ 2$$\sqrt{x}$$ − $$\sqrt{x}$$ ⋅ $$\sqrt{y}$$ + $$\sqrt{y}$$ ⋅ 2$$\sqrt{x}$$ − $$\sqrt{y}$$ ⋅ $$\sqrt{y}$$ = 2$$\sqrt{x²}$$ − $$\sqrt{xy}$$ + 2$$\sqrt{xy}$$ − $$\sqrt{y²}$$ = 2x + $$\sqrt{xy}$$ − y
е) ($$\sqrt{a}$$ − $$\sqrt{b}$$)(3$$\sqrt{a}$$ + 2$$\sqrt{b}$$) = $$\sqrt{a}$$ ⋅ 3$$\sqrt{a}$$ + $$\sqrt{a}$$ ⋅ 2$$\sqrt{b}$$ − $$\sqrt{b}$$ ⋅ 3$$\sqrt{a}$$ − $$\sqrt{b}$$ ⋅ 2$$\sqrt{b}$$ = 3$$\sqrt{a²}$$ + 2$$\sqrt{ab}$$ − 3$$\sqrt{ab}$$ − 2$$\sqrt{b²}$$ = 3a − $$\sqrt{ab}$$ − 2b
ж) (2$$\sqrt{a}$$ + $$\sqrt{b}$$)(3$$\sqrt{a}$$ − 2$$\sqrt{b}$$) = 2$$\sqrt{a}$$ ⋅ 3$$\sqrt{a}$$ − 2$$\sqrt{a}$$ ⋅ 2$$\sqrt{b}$$ + $$\sqrt{b}$$ ⋅ 3$$\sqrt{a}$$ − $$\sqrt{b}$$ ⋅ 2$$\sqrt{b}$$ = 6$$\sqrt{a²}$$ − 4$$\sqrt{ab}$$ + 3$$\sqrt{ab}$$ − 2$$\sqrt{b²}$$ = 6a − $$\sqrt{ab}$$ − 2b
з) (4$$\sqrt{x}$$ − 2$$\sqrt{x}$$)($$\sqrt{x}$$ − $$\sqrt{2x}$$) = 4$$\sqrt{x}$$ ⋅ $$\sqrt{x}$$ − 4$$\sqrt{x}$$ ⋅ $$\sqrt{2x}$$ − $$\sqrt{2x}$$ ⋅ $$\sqrt{x}$$ + $$\sqrt{2x}$$ ⋅ $$\sqrt{2x}$$ = 4$$\sqrt{x²}$$ − 4$$\sqrt{2x²}$$ − $$\sqrt{2x²}$$ + $$\sqrt{4x²}$$ = 4x − 4x$$\sqrt{2}$$ − x$$\sqrt{2}$$ + 2x = 6x − 5x$$\sqrt{2}$$