Let's go through these problems one by one:

1. Simplify each of these algebraic expressions.

a: $3x + 5a - 5x + 2a$

• Combine like terms: $(3x - 5x) + (5a + 2a)$
• Simplified: $-2x + 7a$

b: $3(x + y) - 2(3x - y)$

• Distribute: $3x + 3y - 6x + 2y$
• Combine like terms: $(3x - 6x) + (3y + 2y)$
• Simplified: $-3x + 5y$

c: $2ab - 5bc + 3ab + 7cb$

• Combine like terms: $(2ab + 3ab) + (-5bc + 7cb)$
• Simplified: $5ab + 2bc$

d: $-2x \times 4y + 5xy$

• Multiply: $-8xy + 5xy$
• Simplified: $-3xy$

e: $\frac{45x^2w^2}{15xw^3}$

• Cancel common factors: $\frac{45}{15} \times \frac{x^2}{x} \times \frac{w^2}{w^3}$
• Simplified: $3x \times \frac{1}{w} = \frac{3x}{w}$

f: \frac{169a^b^2c^3}{13a^3b^2c}

• Cancel common factors: \frac{169}{13} \times \frac{a^b^2c^3}{a^3b^2c}
• Simplified: ( 13a^{b^2}/\4 ^ ____ .. "" @path