Question

Factor \[16a 72\] to identify the equivalent expressions. choose 2 answers: choose 2 answers: (choice a) \[4(4a 18)\] a \[4(4a 18)\] (choice b) \[8(2a 9)\] b \[8(2a 9)\] (choice c) \[2(8 36a)\] c \[2(8 36a)\] (choice d) \[2(8a 72)\] d \[2(8a 72)\]

Answer 1

The student needs to factor the expression 16a + 72 by finding the GCF, which is 8. The correct factored expressions are 8(2a + 9) and 4(4a + 18) because both, when expanded, are equivalent to the original expression. The correct answer is b, c.

Step-by-step explanation:

The student is asking to factor the expression 16a + 72 and to choose two equivalent expressions from the given options. In order to factor, we need to find the greatest common factor (GCF) that is divisible by both terms of the expression.

The GCF for 16a and 72 is 8. When we divide both terms in the expression by 8, we get:

[16a ÷ 8 = 2a]

[72 ÷ 8 = 9]

Therefore, the factored form of the expression is 8(2a + 9), so the correct choices are (choice b) 8(2a + 9) and any other equivalent expression. In this case, (choice a) 4(4a + 18) is also equivalent because when expanded, it gives us the original expression 16a + 72. The correct answer is b, c.