Expanding Polynomials

1. \(2x\left( {x - 3} \right)\left( {x + 4} \right)\)
   
   
   Solution

   \(\begin{align}
    2x\left( {x - 3} \right)\left( {x + 4} \right) &= 2x\left( {x^2 + 4x - 3x - 12} \right) \\
     &= 2x\left( {x^2 + x - 12} \right) \\
     &= 2x^3 + 2x^2 - 24x \\
    \end{align}\)
   
   
   
2. \(3ab\left( {a - 3} \right)\left( {a + 3} \right)\)
   
   
   Solution

   \(\begin{align}
    3ab\left( {a - 3} \right)\left( {a + 3} \right) &= 3ab\left( {a^2 + 3a - 3a - 9} \right) \\
     &= 3ab\left( {a^2 - 9} \right) \\
     &= 3a^3 b - 27ab \\
    \end{align}\)
   
   
   
3. \(2\left( {x - 4} \right)^2 + 6\)
   
   
   Solution

   \(\begin{align}
    2\left( {x - 4} \right)^2 + 6 &= 2\left( {x - 4} \right)\left( {x - 4} \right) + 6 \\
     &= 2\left( {x^2 - 4x - 4x + 16} \right) + 6 \\
     &= 2\left( {x^2 - 8x + 16} \right) + 6 \\
     &= 2x^2 - 16x + 32 + 6 \\
     &= 2x^2 - 16x + 38 \\
    \end{align}\)