One way to multiply 47 by 25 is to use a standard multiplication algorithm. We can also do something similar with \((4x+7)(2x+5)\). Just as we multiplied 47 by 5 and then by 20 and then added the results together, we can multiply \(4x+7\) by 5 and then by \(2x\) and then add the results together. Here are two versions:

\(\displaystyle \begin{array}{r} 47 \\ \underline{\times 25} \\ 235 \\ \underline{+ 940} \\ 1175 \end{array}\)

\(\begin{array}{r} 4x + 7 \\ \underline{\times \phantom{0}2x+5} \\ 20x+35 \\ \underline{+ \phantom{0}8x^2 + 14x + \phantom{0}0} \\ 8x^2+34x+35 \\ \end{array}\)
One way to divide 372 by 12 is the standard division algorithm (shown earlier). Another way to do it is by subtraction. To be more efficient, we can take away groups of 120 (ten 12s) until the result is less than 120, and then take away groups of 12. We can take away three groups of 120 and 1 group of 12 from 372, and then we have nothing left over. So there are 31 groups of 12.
1. \(x^2+5x+6=(x+3)(x+2)\)
2. \(x^2+2x-8=(x+4)(x-2)\)

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