615 Представьте в виде суммы: a) $$b^{\frac{1}{3}}c^{\frac{1}{4}}(b^{\frac{2}{3}} + c^{\frac{3}{4}} )$$ б) $$x^{0,5}y^{0,5}(x^{-0,5} - y^{1,5})$$ в) $$(2-y^{1,5}) (2+y^{1,5})$$ г) $$(3p^{0,5}+q^{-1}) (3p^{0,5}-q^{-1})$$ д) $$(1-b^{\frac{1}{2}})^2$$ е) $$(a^{\frac{1}{2}}+2)^2$$ ж) $$(x^{\frac{1}{3}}+y^{\frac{1}{3}})^2$$ з) $$(a^{\frac{1}{2}}-b^{\frac{1}{2}})^2$$ 616 Упростите выражение: a) $$(1+c^{\frac{1}{2}})^2-2c^{\frac{1}{2}}$$ б) $$\sqrt{b} + \sqrt{c}-(b^{\frac{1}{4}}+c^{\frac{1}{4}})^2$$ в) $$(a^{\frac{1}{3}}+b^{\frac{1}{3}})^2-(a^{\frac{1}{3}}-b^{\frac{1}{3}})^2$$ г) $$(x^{\frac{1}{4}}-x^{\frac{1}{3}})^2$$ д) $$(y^{\frac{2}{3}}+3g)^2$$ е) $$(x^{\frac{1}{4}}+1)^2$$ 617 Упростите: a) $$(x^{\frac{1}{2}}-y^{\frac{1}{2}})^2+2x^{\frac{1}{2}}y^{\frac{1}{2}}$$ б) $$(a^{\frac{3}{2}}+5a^{\frac{1}{2}}b^{\frac{1}{2}}+b^{\frac{3}{2}})(a^{\frac{3}{2}}-5a^{\frac{1}{2}}b^{\frac{1}{2}}+b^{\frac{3}{2}})$$

615 Представьте в виде суммы:

a) \[b^{\frac{1}{3}}c^{\frac{1}{4}}(b^{\frac{2}{3}} + c^{\frac{3}{4}}) = b^{\frac{1}{3}}c^{\frac{1}{4}}b^{\frac{2}{3}} + b^{\frac{1}{3}}c^{\frac{1}{4}}c^{\frac{3}{4}} = b^{\frac{1}{3} + \frac{2}{3}}c^{\frac{1}{4}} + b^{\frac{1}{3}}c^{\frac{1}{4} + \frac{3}{4}} = b^1c^{\frac{1}{4}} + b^{\frac{1}{3}}c^1 = bc^{\frac{1}{4}} + b^{\frac{1}{3}}c\] б) \[x^{0.5}y^{0.5}(x^{-0.5} - y^{1.5}) = x^{0.5}y^{0.5}x^{-0.5} - x^{0.5}y^{0.5}y^{1.5} = x^{0.5 - 0.5}y^{0.5} - x^{0.5}y^{0.5 + 1.5} = x^0y^{0.5} - x^{0.5}y^2 = y^{0.5} - x^{0.5}y^2\] в) \[(2-y^{1.5})(2+y^{1.5}) = 4 - (y^{1.5})^2 = 4 - y^3\] г) \[(3p^{0.5}+q^{-1})(3p^{0.5}-q^{-1}) = (3p^{0.5})^2 - (q^{-1})^2 = 9p - q^{-2} = 9p - \frac{1}{q^2}\] д) \[(1-b^{\frac{1}{2}})^2 = 1 - 2b^{\frac{1}{2}} + (b^{\frac{1}{2}})^2 = 1 - 2b^{\frac{1}{2}} + b\] е) \[(a^{\frac{1}{2}}+2)^2 = (a^{\frac{1}{2}})^2 + 4a^{\frac{1}{2}} + 4 = a + 4a^{\frac{1}{2}} + 4\] ж) \[(x^{\frac{1}{3}}+y^{\frac{1}{3}})^2 = (x^{\frac{1}{3}})^2 + 2x^{\frac{1}{3}}y^{\frac{1}{3}} + (y^{\frac{1}{3}})^2 = x^{\frac{2}{3}} + 2x^{\frac{1}{3}}y^{\frac{1}{3}} + y^{\frac{2}{3}}\] з) \[(a^{\frac{1}{2}}-b^{\frac{1}{2}})^2 = (a^{\frac{1}{2}})^2 - 2a^{\frac{1}{2}}b^{\frac{1}{2}} + (b^{\frac{1}{2}})^2 = a - 2a^{\frac{1}{2}}b^{\frac{1}{2}} + b\]

616 Упростите выражение:

a) \[(1+c^{\frac{1}{2}})^2 - 2c^{\frac{1}{2}} = 1 + 2c^{\frac{1}{2}} + c - 2c^{\frac{1}{2}} = 1 + c\] б) \[\sqrt{b} + \sqrt{c} - (b^{\frac{1}{4}} + c^{\frac{1}{4}})^2 = \sqrt{b} + \sqrt{c} - (b^{\frac{1}{2}} + 2b^{\frac{1}{4}}c^{\frac{1}{4}} + c^{\frac{1}{2}}) = \sqrt{b} + \sqrt{c} - \sqrt{b} - 2b^{\frac{1}{4}}c^{\frac{1}{4}} - \sqrt{c} = -2b^{\frac{1}{4}}c^{\frac{1}{4}}\] в) \[(a^{\frac{1}{3}}+b^{\frac{1}{3}})^2 - (a^{\frac{1}{3}}-b^{\frac{1}{3}})^2 = (a^{\frac{2}{3}} + 2a^{\frac{1}{3}}b^{\frac{1}{3}} + b^{\frac{2}{3}}) - (a^{\frac{2}{3}} - 2a^{\frac{1}{3}}b^{\frac{1}{3}} + b^{\frac{2}{3}}) = a^{\frac{2}{3}} + 2a^{\frac{1}{3}}b^{\frac{1}{3}} + b^{\frac{2}{3}} - a^{\frac{2}{3}} + 2a^{\frac{1}{3}}b^{\frac{1}{3}} - b^{\frac{2}{3}} = 4a^{\frac{1}{3}}b^{\frac{1}{3}}\] г) \[(x^{\frac{1}{4}}-x^{\frac{1}{3}})^2 = (x^{\frac{1}{4}})^2 - 2x^{\frac{1}{4}}x^{\frac{1}{3}} + (x^{\frac{1}{3}})^2 = x^{\frac{1}{2}} - 2x^{\frac{7}{12}} + x^{\frac{2}{3}}\] д) \[(y^{\frac{2}{3}}+3g)^2 = (y^{\frac{2}{3}})^2 + 6gy^{\frac{2}{3}} + 9g^2 = y^{\frac{4}{3}} + 6gy^{\frac{2}{3}} + 9g^2\] е) \[(x^{\frac{1}{4}}+1)^2 = (x^{\frac{1}{4}})^2 + 2x^{\frac{1}{4}} + 1 = x^{\frac{1}{2}} + 2x^{\frac{1}{4}} + 1\]

617 Упростите:

a) \[(x^{\frac{1}{2}}-y^{\frac{1}{2}})^2 + 2x^{\frac{1}{2}}y^{\frac{1}{2}} = (x - 2x^{\frac{1}{2}}y^{\frac{1}{2}} + y) + 2x^{\frac{1}{2}}y^{\frac{1}{2}} = x + y\] б) \[(a^{\frac{3}{2}}+5a^{\frac{1}{2}}b^{\frac{1}{2}}+b^{\frac{3}{2}})(a^{\frac{3}{2}}-5a^{\frac{1}{2}}b^{\frac{1}{2}}+b^{\frac{3}{2}}) = ((a^{\frac{3}{2}}+b^{\frac{3}{2}}) + 5a^{\frac{1}{2}}b^{\frac{1}{2}})((a^{\frac{3}{2}}+b^{\frac{3}{2}}) - 5a^{\frac{1}{2}}b^{\frac{1}{2}}) = (a^{\frac{3}{2}}+b^{\frac{3}{2}})^2 - (5a^{\frac{1}{2}}b^{\frac{1}{2}})^2 = a^3 + 2a^{\frac{3}{2}}b^{\frac{3}{2}} + b^3 - 25ab = a^3 + 2a^{\frac{3}{2}}b^{\frac{3}{2}} + b^3 - 25ab\]