1. **State the problem:** Simplify the expression $$(5g+2)(g-1)-(3+g)(2g-7)$$. 2. **Use the distributive property (FOIL) to expand each product:** $$(5g+2)(g-1) = 5g \cdot g + 5g \cdot (-1) + 2 \cdot g + 2 \cdot (-1) = 5g^2 - 5g + 2g - 2$$ $$(3+g)(2g-7) = 3 \cdot 2g + 3 \cdot (-7) + g \cdot 2g + g \cdot (-7) = 6g - 21 + 2g^2 - 7g$$ 3. **Rewrite the original expression with expanded terms:** $$5g^2 - 5g + 2g - 2 - (6g - 21 + 2g^2 - 7g)$$ 4. **Distribute the minus sign to the second group:** $$5g^2 - 5g + 2g - 2 - 6g + 21 - 2g^2 + 7g$$ 5. **Combine like terms:** - Combine $5g^2$ and $-2g^2$: $$5g^2 - 2g^2 = \cancel{5g^2} - \cancel{2g^2} + 3g^2$$ - Combine $-5g$, $2g$, $-6g$, and $7g$: $$-5g + 2g - 6g + 7g = (-5 + 2 - 6 + 7)g = (-5 + 2)g + (-6 + 7)g = (-3)g + (1)g = -3g + g = -2g$$ - Combine constants $-2$ and $21$: $$-2 + 21 = 19$$ 6. **Final simplified expression:** $$3g^2 - 2g + 19$$