Expand Brackets

1. Expand $3(x+2)$: $$3x + 6$$ 2. Expand $x(x-1)$: $$x^2 - x$$ 3. Expand $-2(3-x)$: $$-6 + 2x$$ 4. Expand $-2x(5-3x)$: $$-10x + 6x^2$$ 5. Expand $x^2 (x-3)$: $$x^3 - 3x^2$$ 6. Expand $x^2 (x^2-3x)$: $$x^4 - 3x^3$$ 7. Expand $3xy(3x-y)$: $$9x^2y - 3xy^2$$ 8. Expand $-3xy(4y^2-2xy)$: $$-12xy^3 + 6x^2y^2$$ 9. Expand $(x+1)(x+2)$: $$x^2 + 3x + 2$$ 10. Expand $(x-3)(x+2)$: $$x^2 - x - 6$$ 11. Expand $(x-5)(x-4)$: $$x^2 - 9x + 20$$ 12. Expand $2(x+1)(x-2)$: First expand $(x+1)(x-2) = x^2 - x - 2$ Then multiply by 2: $$2x^2 - 2x - 4$$ 13. Expand $x(x-3)(x+2)$: First expand $(x-3)(x+2) = x^2 - x - 6$ Then multiply by $x$: $$x^3 - x^2 - 6x$$ 14. Expand $2x(3-x)(x^2+2)$: First expand $(3-x)(x^2+2) = 3x^2 + 6 - x^3 - 2x = -x^3 + 3x^2 - 2x + 6$ Then multiply by $2x$: $$-2x^4 + 6x^3 - 4x^2 + 12x$$ 15. Expand $3x^2 (3x^2-5)(4-x^2)$: First expand $(3x^2-5)(4-x^2) = 12x^2 - 3x^4 - 20 + 5x^2 = -3x^4 + 17x^2 - 20$ Then multiply by $3x^2$: $$-9x^6 + 51x^4 - 60x^2$$ 16. Expand $-(x+3)(2-x)$: First expand $(x+3)(2-x) = 2x + 6 - x^2 - 3x = -x^2 - x + 6$ Then apply negative sign: $$x^2 + x - 6$$ 17. Expand $(x+3)(x^2+2x+3)$: $$x^3 + 2x^2 + 3x + 3x^2 + 6x + 9 = x^3 + 5x^2 + 9x + 9$$ 18. Expand $(2x-3)(x^2-2x-3)$: $$2x^3 - 4x^2 - 6x - 3x^2 + 6x + 9 = 2x^3 - 7x^2 + 9$$ 19. Expand $(x+1)^2$: $$x^2 + 2x + 1$$ 20. Expand $(x-2)^3$: $$(x-2)(x-2)^2 = (x-2)(x^2 - 4x + 4) = x^3 - 4x^2 + 4x - 2x^2 + 8x - 8 = x^3 - 6x^2 + 12x - 8$$ 21. Expand $-(2x^2-3)^2$: $$(2x^2 - 3)^2 = 4x^4 - 12x^2 + 9$$ Apply negative sign: $$-4x^4 + 12x^2 - 9$$ 22. Expand $-2x(x^2+2x+3)^2$: First expand $(x^2+2x+3)^2 = x^4 + 4x^3 + 10x^2 + 12x + 9$ Then multiply by $-2x$: $$-2x^5 - 8x^4 - 20x^3 - 24x^2 - 18x$$ 23. Expand $(x + \frac{1}{x})^2$: $$x^2 + 2 + \frac{1}{x^2}$$ 24. Expand $(x + \frac{1}{\sqrt{x}})^2$: $$x^2 + 2x^{\frac{1}{2}} + x^{-1}$$ Final answers are the expanded forms above.