\begin{tabular}{|c|l|}\hline 26. & \( (2 a+b)^{3}= \) \\ \hline 27. & \( (2 x-5)^{3}= \) \\ \hline 28. & \( (a-b)^{3}=a^{2}-3 a^{2} b-7 a b-b \) \\ \hline 29. & \( (3 a-5)^{3}= \) \\ \hline\end{tabular}

To expand the expressions given in the table, we can use the binomial theorem or the formula for the cube of a binomial, which states that: \[ (x+y)^3 = x^3 + 3x^2y + 3xy^2 + y^3 \] Let's apply this to each expression: ### 26. \( (2a + b)^3 \) Using the formula: - Let \( x = 2a \) and \( y = b \). - Then, we have: \[ (2a + b)^3 = (2a)^3 + 3(2a)^2(b) + 3(2a)(b^2) + b^3 \] Calculating each term: - \( (2a)^3 = 8a^3 \) - \( 3(2a)^2b = 3 \cdot 4a^2b = 12a^2b \) - \( 3(2a)(b^2) = 6ab^2 \) - \( b^3 = b^3 \) Putting it all together: \[ (2a + b)^3 = 8a^3 + 12a^2b + 6ab^2 + b^3 \] ### 27. \( (2x - 5)^3 \) Using the formula: - Let \( x = 2x \) and \( y = -5 \). - Then, we have: \[ (2x - 5)^3 = (2x)^3 + 3(2x)^2(-5) + 3(2x)(-5)^2 + (-5)^3 \] Calculating each term: - \( (2x)^3 = 8x^3 \) - \( 3(2x)^2(-5) = 3 \cdot 4x^2(-5) = -60x^2 \) - \( 3(2x)(-5)^2 = 3(2x)(25) = 150x \) - \( (-5)^3 = -125 \) Putting it all together: \[ (2x - 5)^3 = 8x^3 - 60x^2 + 150x - 125 \] ### 28. \( (a - b)^3 = a^2 - 3a^2b - 7ab - b \) This expression seems incorrect. The correct expansion of \( (a - b)^3 \) is: Using the formula: \[ (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 \] So, the correct expansion is: \[ (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 \] ### 29. \( (3a - 5)^3 \) Using the formula: - Let \( x = 3a \) and \( y = -5 \). - Then, we have: \[ (3a - 5)^3 = (3a)^3 + 3(3a)^2(-5) + 3(3a)(-5)^2 + (-5)^3 \] Calculating each term: - \( (3a)^3 = 27a^3 \) - \( 3(3a)^2(-5) = 3 \cdot 9a^2(-5) = -135a^2 \) - \( 3(3a)(-5)^2 = 3(3a)(25) = 225a \) - \( (-5)^3 = -125 \) Putting it all together: \[ (3a - 5)^3 = 27a^3 - 135a^2 + 225a - 125 \] ### Summary of Results \[ \begin{tabular}{|c|l|} \hline 26. & \( (2a + b)^3 = 8a^3 + 12a^2b + 6ab^2 + b^3 \) \\ \hline 27. & \( (2x - 5)^3 = 8x^3 - 60x^2 + 150x - 125 \) \\ \hline 28. & \( (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 \) \\ \hline 29. & \( (3a - 5)^3 = 27a^3 - 135a^2 +