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Factor 
16 a+72 to identify the equivalent expressions.
Choose 2 answers:
A 
4(4a+18)
B 
8(2a+9)
c 
2(8+36 a)
D 
2(8a+72)

Factor 16a+72 16 a+72 to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 4(4a+18) 4(4 a+18) \newlineB 8(2a+9) 8(2 a+9) \newlineC 2(8+36a) 2(8+36 a) \newlineD 2(8a+72) 2(8 a+72)

Full solution

Q. Factor 16a+72 16 a+72 to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 4(4a+18) 4(4 a+18) \newlineB 8(2a+9) 8(2 a+9) \newlineC 2(8+36a) 2(8+36 a) \newlineD 2(8a+72) 2(8 a+72)
  1. Identify GCF of terms: Identify the greatest common factor (GCF) of the terms 16a16a and 7272.\newlineThe GCF of 1616 and 7272 is 88, since 88 is the largest number that divides both 1616 and 7272 without leaving a remainder.
  2. Factor out GCF from each term: Factor out the GCF from each term.\newlineWe can write 16a16a as 8(2a)8(2a) and 7272 as 8(9)8(9), so factoring out the GCF gives us:\newline16a+72=8(2a)+8(9)16a + 72 = 8(2a) + 8(9)
  3. Combine terms inside parentheses: Combine the terms inside the parentheses.\newlineSince we have factored out an 88 from both terms, we can combine them into a single term inside the parentheses:\newline16a+72=8(2a+9)16a + 72 = 8(2a + 9)
  4. Check equivalent answer choices: Check the answer choices to see which ones are equivalent to the factored expression.\newlineWe have factored the expression as 8(2a+9)8(2a + 9), so we need to check which answer choices match this expression.\newlineA) 4(4a+18)4(4a+18) is not equivalent because 44 is not the GCF.\newlineB) 8(2a+9)8(2a+9) is equivalent because it matches our factored expression.\newlineC) 2(8+36a)2(8+36a) is not equivalent because the terms inside the parentheses are not in the correct order, and the GCF is not factored out correctly.\newlineD) 2(8a+72)2(8a+72) is not equivalent because the GCF is not factored out correctly.

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