1. **State the problem:** Simplify the algebraic expression $$7xy - 5x^2 - 6y + 2x + 5xy - 3x - 13zy + 3x^3 + 4y - 5x^2 - 4zy + 5x^3$$. 2. **Group like terms:** Combine terms with the same variables and powers. - Terms with $x^3$: $$3x^3 + 5x^3$$ - Terms with $x^2$: $$-5x^2 - 5x^2$$ - Terms with $xy$: $$7xy + 5xy$$ - Terms with $x$: $$2x - 3x$$ - Terms with $y$: $$-6y + 4y$$ - Terms with $zy$: $$-13zy - 4zy$$ 3. **Add or subtract coefficients:** - $x^3$ terms: $$3x^3 + 5x^3 = 8x^3$$ - $x^2$ terms: $$-5x^2 - 5x^2 = -10x^2$$ - $xy$ terms: $$7xy + 5xy = 12xy$$ - $x$ terms: $$2x - 3x = \cancel{2x} - \cancel{3x} = -1x = -x$$ - $y$ terms: $$-6y + 4y = -2y$$ - $zy$ terms: $$-13zy - 4zy = -17zy$$ 4. **Write the simplified expression:** $$8x^3 - 10x^2 + 12xy - x - 2y - 17zy$$ This is the simplified form of the given expression.