1. **Problem statement:** Simplify each algebraic expression by combining like terms. 2. **Formula and rules:** Like terms have the same variable raised to the same power. To simplify, add or subtract their coefficients. 3. **Step-by-step simplifications:** (a) $3a + 2b + 4a + b$ Combine like terms $a$ and $b$: $$3a + 4a = 7a$$ $$2b + b = 3b$$ Simplified: $$7a + 3b$$ (b) $7y + 5y + 2h + 2h$ Combine like terms $y$ and $h$: $$7y + 5y = 12y$$ $$2h + 2h = 4h$$ Simplified: $$12y + 4h$$ (c) $g + 8a + 2a + g$ Combine like terms $g$ and $a$: $$g + g = 2g$$ $$8a + 2a = 10a$$ Simplified: $$2g + 10a$$ (g) $2y + 4 + 3y - 1$ Combine like terms $y$ and constants: $$2y + 3y = 5y$$ $$4 - 1 = 3$$ Simplified: $$5y + 3$$ (h) $8 + 3w - w - 3$ Combine like terms $w$ and constants: $$3w - w = 2w$$ $$8 - 3 = 5$$ Simplified: $$2w + 5$$ (i) $5 - 45 - 2 + 10s$ Combine constants: $$5 - 45 = -40$$ $$-40 - 2 = -42$$ Simplified: $$-42 + 10s$$ (m) $3a - 2b + a - 5b$ Combine like terms $a$ and $b$: $$3a + a = 4a$$ $$-2b - 5b = -7b$$ Simplified: $$4a - 7b$$ (n) $2x - 2y - 6x + 5y$ Combine like terms $x$ and $y$: $$2x - 6x = \cancel{2x} - 6x = -4x$$ $$-2y + 5y = 3y$$ Simplified: $$-4x + 3y$$ (o) $y - 4m - 3y - 5m$ Combine like terms $y$ and $m$: $$y - 3y = -2y$$ $$-4m - 5m = -9m$$ Simplified: $$-2y - 9m$$