Answer: Yes they are equivalent
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The reason why is because
4(5d - 4) = 4*(5d) + 4(-4) = 20d - 16
You multiply the outer term 4 by each term inside the parenthesis
4 times 5d = 4*5d = 20d
4 times -4 = 4*(-4) = -16
I'm using the distributive property.
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Alternatively, you can start with 20d - 16 and factor out the GCF 4. Divide each term by 4 to get
20d/4 = 5d
-16/4 = -4
So after dividing each term of 20d-16 by 4, we get 5d-4 and the 4 will be pulled out to say 20d - 16 = 4(5d - 4)
As you can probably see, factoring is just thinking of distributing in reverse. Instead of multiplying each term by the same number, you divide each term by the same number. You can distribute the 4 back in to check your factorization.
