Expand Polynomial 17Cb49

1. **State the problem:** We are asked to expand and simplify the expression $(x+y)(7x+2y-1)$ and verify if it equals $7x^2+2xy+2y^2-x-y$. 2. **Recall the distributive property:** $$(a+b)(c+d+e) = a(c+d+e) + b(c+d+e)$$ 3. **Apply the distributive property:** $$(x+y)(7x+2y-1) = x(7x+2y-1) + y(7x+2y-1)$$ 4. **Multiply each term:** $$x \cdot 7x = 7x^2$$ $$x \cdot 2y = 2xy$$ $$x \cdot (-1) = -x$$ $$y \cdot 7x = 7xy$$ $$y \cdot 2y = 2y^2$$ $$y \cdot (-1) = -y$$ 5. **Combine all terms:** $$7x^2 + 2xy - x + 7xy + 2y^2 - y$$ 6. **Combine like terms:** $$2xy + 7xy = 9xy$$ 7. **Final simplified expression:** $$7x^2 + 9xy + 2y^2 - x - y$$ 8. **Compare with given expression:** Given: $$7x^2 + 2xy + 2y^2 - x - y$$ Our result: $$7x^2 + 9xy + 2y^2 - x - y$$ They are not equal because the coefficient of $xy$ differs ($2xy$ vs $9xy$). **Answer:** The expanded form of $(x+y)(7x+2y-1)$ is $$7x^2 + 9xy + 2y^2 - x - y$$ which does not equal $$7x^2 + 2xy + 2y^2 - x - y$$.