1. Problem: Expand and simplify $$3(x+4) + 6(4 - 3x)$$ Step 1: Distribute terms inside parentheses: $$3x + 12 + 24 - 18x$$ Step 2: Combine like terms: $$(3x - 18x) + (12 + 24) = -15x + 36$$ 2. Problem: Rewrite $$5x + 10$$ by factoring out the common factor. Step 1: Identify the common factor (5): $$5(x + 2)$$ 3. Problem: Expand and simplify $$-2(3y - 5) - 3(-4y - 5)$$ Step 1: Distribute the negatives: $$-6y + 10 + 12y + 15$$ Step 2: Combine like terms: $$( -6y + 12y ) + (10 + 15) = 6y + 25$$ 4. Problem: Expand $$4(2x + 3y - 5)$$ Step 1: Distribute 4: $$8x + 12y - 20$$ 5. Problem: Simplify $$x + 3 + 5 + 2x$$ using commutative and associative properties. Step 1: Group like terms: $$(x + 2x) + (3 + 5)$$ Step 2: Simplify: $$3x + 8$$ 6. Problem: Rewrite $$7a + 5b - 2a + 3b$$ grouping like terms using associative law. Step 1: Group like terms: $$(7a - 2a) + (5b + 3b)$$ Step 2: Simplify: $$5a + 8b$$ 7. Problem: Factor out common terms from $$6m + 9n - 3m$$ using distributive law. Step 1: Combine like terms: $$(6m - 3m) + 9n = 3m + 9n$$ Step 2: Factor out common factor 3: $$3(m + 3n)$$ 8. Problem: Simplify $$2(x + 5) + 3(x + 5)$$ by factoring. Step 1: Recognize common factor $$(x + 5)$$ Step 2: Factor out $$(x + 5)$$: $$(2 + 3)(x + 5) = 5(x + 5)$$ 9. Problem: Simplify $$5(2p + 3) + 4(2p + 3)$$ applying distribution and combining like terms. Step 1: Distribute each term: $$10p + 15 + 8p + 12$$ Step 2: Combine like terms: $$(10p + 8p) + (15 + 12) = 18p + 27$$ 10. Problem: Expand and simplify $$3(x+4) + 6(4 - 3x) - 2(4x - 7)$$ Step 1: Distribute each term: $$3x + 12 + 24 - 18x - 8x + 14$$ Step 2: Combine like terms: $$(3x - 18x - 8x) + (12 + 24 + 14) = -23x + 50$$