Question

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

a. 4d + 12e
b. 18x + 30y
c. 21a +28y
d. 24f + 56g

Answer 1

a)

`4=\textcircled{2} * \textcircled{2} \\ 12=\textcircled{2} * \textcircled{2} * 3 \\ GCF(4,12)=2 * 2=4 \\ \\ 4d+12e=4 * d+4 * 3e=4(d+3e)`

b)

`18=\textcircled{2} * \textcircled{3} * 3 \\ 30=\textcircled{2} * \textcircled{3} * 5 \\ GCF(18,30)=2 * 3=6 \\ \\ 18x+30y=6 * 3x + 6 * 5y=6(3x+5y)`

c)

`21=3 * \textcircled{7} \\ 28=2 * 2 * \textcircled{7} \\ GCF(21,28)=7 \\ \\ 21a+28y=7 * 3a+4 * 4y=7(3a+4y)`

d)

`24=\textcircled{2} * \textcircled{2} * \textcircled{2} * 3 \\ 56=\textcircled{2} * \textcircled{2} * \textcircled{2} * 7 \\ GCF(24,56)=2 * 2 * 2=8 \\ \\ 24f+56g=8 * 3f+8 * 7g=8(3f+7g)`