Factorization the given algebraic expression 16a + 72, we get the expression 8(2a + 9), which is equivalent to the expressions 4(4a + 18) and 8(2a + 9), that is, to options A and B. Hence, options A and B are the right choices.
What is factorization?
Factorization is the process of representing an algebraic expression as the product of two or more expressions, which when multiplied, give back the same expression.
How to solve the given question?
In the question, we are asked to factor the expression 16a + 72, to identify a similar expression from the given options.
The expression 16a + 72 is made of two terms 16a and 72.
To factor the expression 16a + 72, we take common factors between the two terms.
We get 8 as common between the two expressions from the constants, and no variables common.
Taking 8 as common, we can write this expression in the way: 8(2a + 9).
Now, we check the given options for equivalent expressions:
- A. 4(4a + 18): Can be further factored to 8(2a + 9), by taking 2 as common between 4a and 18. Hence is equivalent to 16a + 72.
- B. 8(2a + 9): Is equivalent to 16a + 72.
- C. 2(8 + 36a): Can be further factored to 8(2 + 9a), by taking 4 as common between 8 and 36a. But, this is not equivalent to 16a + 72.
- D. 2(8a + 72): Can be further factored to 16(a + 9), by taking 8 as common between 8a and 72. But, this is not equivalent to 16a + 72.
Hence, options A and B are the right choices.
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