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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

Sagot :

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a)
[tex]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)[/tex]

b)
[tex]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)[/tex]

c)
[tex]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)[/tex]

d)
[tex]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)[/tex]
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