Question

Use GCF and the distributive property to write equivalent expressions in factored form for the following expressions.

Answer 1

A)
$4=\textcircled{2} \times \textcircled{2} \\ 12=\textcircled{2} \times \textcircled{2} \times 3 \\ GCF(4,12)=2 \times 2=4 \\ \\ 4d+12e=4 \times d+4 \times 3e=4(d+3e)$

b)
$18=\textcircled{2} \times \textcircled{3} \times 3 \\ 30=\textcircled{2} \times \textcircled{3} \times 5 \\ GCF(18,30)=2 \times 3=6 \\ \\ 18x+30y=6 \times 3x + 6 \times 5y=6(3x+5y)$

c)
$21=3 \times \textcircled{7} \\ 28=2 \times 2 \times \textcircled{7} \\ GCF(21,28)=7 \\ \\ 21a+28y=7 \times 3a+4 \times 4y=7(3a+4y)$

d)
$24=\textcircled{2} \times \textcircled{2} \times \textcircled{2} \times 3 \\ 56=\textcircled{2} \times \textcircled{2} \times \textcircled{2} \times 7 \\ GCF(24,56)=2 \times 2 \times 2=8 \\ \\ 24f+56g=8 \times 3f+8 \times 7g=8(3f+7g)$