Question

Write the sum of the numbers as the product of their GCF and another sum. Show your work. Can you guys help me please and explain it to me. I don’t get it. Thank You!
56+64_________

30+54_________

Answer 1

The distributive property: a(b + c) = ab + ac

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Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56

Factors of  64: 1, 2, 4, 8, 16, 32, 64

GCF(56, 64) = 8

56 = 8 · 7

64 = 8 · 8

56 + 64 = 8 · 7 + 8 · 8 = = 8(7 + 8)

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Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

GCF(30, 54) = 6

30 = 6 · 5

54 = 6 · 9

30 + 54 =  6 · 5 + 6 · 9 = 6(5 + 9)