3 × (4 + 5) = 3 × 4 + 3 × 5 ; Apply the distributive property
= 12 + 15 ; Multiply 3 × 4 and 3 × 5
= 27 ; Add 12 + 15

2.5 × (6 – 2) = 2.5 × 6 – 2.5 × 2 ; Apply the distributive property
= 15 – 5 ; Multiply 2.5 × 6 and 2.5 × 2
= 10 ; Subtract 5 from 15

1/2 × (8 + 12) = 1/2 × 8 + 1/2 × 12 ; Apply the distributive property
= 4 + 6 ; Multiply 1/2 × 8 and 1/2 × 12
= 10 ; Add 4 + 6

2(x + 3) = 2 × x + 2 × 3 ; Apply the distributive property
= 2x + 6 ; Multiply 2 × x and 2 × 3

(4 + x)3 = 4 × 3 + x × 3 ; Apply the distributive property
= 12 + 3x ; Multiply 4 × 3 and x × 3

5(x – 2) = 5 × x – 5 × 2 ; Apply the distributive property
= 5x – 10 ; Multiply 5 × x and 5 × 2

2(x + 3) + 4(x + 5) = 2x + 6 + 4x + 20 ; Apply the distributive property
= 6x + 26 ; Combine like terms

3(x – 2) + 5(x + 4) = 3x – 6 + 5x + 20 ; Apply the distributive property
= 8x + 14 ; Combine like terms

-2(x + 1) + 3(x – 3) = -2x – 2 + 3x – 9 ; Apply the distributive property
= x – 11 ; Combine like terms

2.5(x + 1.2) + 3.5(x + 0.8)
= 2.5x + 2.5 * 1.2 + 3.5x + 3.5 * 0.8 ; Apply the distributive property
= 2.5x + 3 + 3.5x + 2.8
= 6x + 5.8 ; Combine like terms

1.5(x – 0.5) + 2.5(x + 1.5)
= 1.5x – 1.5 * 0.5 + 2.5x + 2.5 * 1.5 ; Apply the distributive property
= 1.5x – 0.75 + 2.5x + 3.75
= 4x + 3 ; Combine like terms

-1.2(x + 2.5) + 0.6(x – 1.5)
= -1.2x – 1.2 * 2.5 + 0.6x – 0.6 * 1.5 ; Apply the distributive property
= -1.2x – 3 + 0.6x – 0.9
= -0.6x – 3.9 ; Combine like terms

\(\frac{1}{2}(x + \frac{1}{3}) + \frac{2}{3}(x + \frac{1}{4})\) ; Given expression
\(= \frac{1}{2}x + \frac{1}{2} \cdot \frac{1}{3} + \frac{2}{3}x + \frac{2}{3} \cdot \frac{1}{4}\) ; Apply the distributive property to both terms
\(= \frac{1}{2}x + \frac{1}{6} + \frac{2}{3}x + \frac{1}{6}\) ; Multiply the fractions inside the parentheses
\(= \frac{7}{6}x + \frac{1}{3}\) ; Combine like terms to get the final result

\(\frac{3}{4}(x – \frac{1}{2}) + \frac{1}{4}(x + \frac{1}{3})\) ; Given expression
\(= \frac{3}{4}x – \frac{3}{4} \cdot \frac{1}{2} + \frac{1}{4}x + \frac{1}{4} \cdot \frac{1}{3}\) ; Apply the distributive property to both terms
\(= \frac{3}{4}x – \frac{3}{8} + \frac{1}{4}x + \frac{1}{12}\) ; Multiply the fractions inside the parentheses
\(= \frac{4}{3}x – \frac{1}{4}\) ; Combine like terms to get the final result

\(\frac{2}{3}(x + \frac{3}{5}) – \frac{1}{5}(x – \frac{2}{3})\) ; Given expression
\(= \frac{2}{3}x + \frac{2}{3} \cdot \frac{3}{5} – \frac{1}{5}x + \frac{1}{5} \cdot \frac{2}{3}\) ; Apply the distributive property to both terms
\(= \frac{2}{3}x + \frac{2}{5} – \frac{1}{5}x + \frac{2}{15}\) ; Multiply the fractions inside the parentheses
\(= \frac{7}{15}x + \frac{8}{15}\) ; Combine like terms to get the final result

\(2(3x + 4)\) ; Given expression
\(= 2 \cdot 3x + 2 \cdot 4\) ; Apply the distributive property
\(= 6x + 8\) ; Multiply the constants to get the final result

\(\frac{1}{2}(4x – 3)\) ; Given expression
\(= \frac{1}{2} \cdot 4x – \frac{1}{2} \cdot 3\) ; Apply the distributive property
\(= 2x – \frac{3}{2}\) ; Multiply the constants to get the final result

\(-3(5x + \frac{1}{3})\) ; Given expression
\(= -3 \cdot 5x – 3 \cdot \frac{1}{3}\) ; Apply the distributive property
\(= -15x – 1\) ; Multiply the constants to get the final result

\(4(-2x + \frac{5}{2})\) ; Given expression
\(= 4 \cdot -2x + 4 \cdot \frac{5}{2}\) ; Apply the distributive property
\(= -8x + 10\) ; Multiply the constants to get the final result

\(\frac{3}{4}(-\frac{1}{2}x + 6)\) ; Given expression
\(= \frac{3}{4} \cdot -\frac{1}{2}x + \frac{3}{4} \cdot 6\) ; Apply the distributive property
\(= -\frac{3}{8}x + \frac{9}{2}\) ; Multiply the constants to get the final result