Q. Factor 16a+72 to identify the equivalent expressions.Choose 2 answers:A 4(4a+18)B 8(2a+9)C 2(8+36a)D 2(8a+72)
Identify GCF of terms: Identify the greatest common factor (GCF) of the terms 16a and 72.The GCF of 16 and 72 is 8, since 8 is the largest number that divides both 16 and 72 without leaving a remainder.
Factor out GCF from each term: Factor out the GCF from each term.We can write 16a as 8(2a) and 72 as 8(9), so factoring out the GCF gives us:16a+72=8(2a)+8(9)
Combine terms inside parentheses: Combine the terms inside the parentheses.Since we have factored out an 8 from both terms, we can combine them into a single term inside the parentheses:16a+72=8(2a+9)
Check equivalent answer choices: Check the answer choices to see which ones are equivalent to the factored expression.We have factored the expression as 8(2a+9), so we need to check which answer choices match this expression.A) 4(4a+18) is not equivalent because 4 is not the GCF.B) 8(2a+9) is equivalent because it matches our factored expression.C) 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.D) 2(8a+72) is not equivalent because the GCF is not factored out correctly.
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