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\((x+2)(x+3)\)

\(x\) \(3\)
\(x\) \(x^2\) \(3x\)
\(2\) \(2x\) \(6\)
\begin{align}x^2 + 3x + 2x + 6\\ x^2 + 5x + 6 \end{align}

\((x+4)(x-1)\)

\(x\) \(4\)
\(x\) \(x^2\) \(4x\)
\(-1\) \(-x\) \(-4\)
\begin{align}x^2 - x + 4x - 4\\ x^2 + 3x - 4 \end{align}

\((2x+3)(x+4)\)

\(x\) \(4\)
\(2x\) \(2x^2\) \(8x\)
\(3\) \(3x\) \(12\)
\begin{align}2x^2 + 3x + 8x + 12\\ 2x^2 + 11x + 12 \end{align}

\((3x+4)(2x-5)\)

\(2x\) \(-5\)
\(3x\) \(6x^2\) \(-15x\)
\(4\) \(8x\) \(-20\)
\begin{align}6x^2 + 8x - 15x - 20\\ 6x^2 - 7x - 20 \end{align}