Question

question
which expression is equivalent to 36 + 12?
answer
○ 3(12 + 9)
○ 4(9 + 3)
○ 2(18 + 12)
○ 6(30 + 2)

Explanation:

Step1: Analyze each option

First, we need to expand each option using the distributive property \(a(b + c)=ab+ac\) and check if it equals \(36 + 12\).

Step2: Check option 1: \(3(12 + 9)\)

Expand \(3(12+9)\) using distributive property: \(3\times12+3\times9 = 36+27
eq36 + 12\).

Step3: Check option 2: \(2(18 + 12)\)

Expand \(2(18 + 12)\) using distributive property: \(2\times18+2\times12=36 + 24
eq36+12\).

Step4: Check option 3: \(4(9 + 3)\)

Expand \(4(9 + 3)\) using distributive property: \(4\times9+4\times3 = 36+12\), which is equal to the given expression \(36 + 12\). Wait, but in the original options, maybe I misread. Wait, the original options: first option is \(3(12 + 9)\), second \(2(18+12)\), third \(4(9 + 3)\), fourth \(6(30 + 2)\)? Wait, no, the user's image: the options are \(3(12 + 9)\), \(2(18 + 12)\), \(4(9 + 3)\), \(6(30 + 2)\)? Wait, no, let's re - check. Wait the question is which expression is equivalent to \(36+12\). Let's factor \(36 + 12\). The greatest common factor of 36 and 12 is 12? No, 36 and 12: GCF of 36 and 12 is 12? Wait 36 = 12×3, 12 = 12×1, so \(36 + 12=12(3 + 1)\)? No, wait 36+12 = 48. Wait 3(12 + 9)=3×21 = 63, 2(18 + 12)=2×30 = 60, 4(9 + 3)=4×12 = 48, 6(30+2)=6×32 = 192. Wait \(36 + 12=48\), and \(4(9 + 3)=48\). But wait, maybe I made a mistake. Wait \(36+12 = 48\), \(4(9 + 3)=4\times12 = 48\). But let's check again. Wait the options: the first option is \(3(12 + 9)=3\times21 = 63\), second \(2(18 + 12)=2\times30 = 60\), third \(4(9 + 3)=4\times12 = 48\), fourth \(6(30 + 2)=6\times32 = 192\). But \(36+12 = 48\), so \(4(9 + 3)\) is equivalent. But wait, maybe the options are different. Wait, no, maybe I misread the options. Wait the user's image: the options are \(3(12 + 9)\), \(2(18 + 12)\), \(4(9 + 3)\), \(6(30 + 2)\)? Wait, no, let's re - check the original problem. Wait the question is "Which expression is equivalent to \(36 + 12\)". Let's factor \(36+12\). We can factor out 12: \(12(3 + 1)\), but that's not an option. Or factor out 6: \(6(6 + 2)\), not an option. Factor out 4: \(4(9+3)\), because \(4\times9 = 36\) and \(4\times3 = 12\), so \(4(9 + 3)=36+12\). So the correct option is \(4(9 + 3)\). But in the user's image, the options are: first \(3(12 + 9)\), second \(2(18 + 12)\), third \(4(9 + 3)\), fourth \(6(30 + 2)\). So the correct answer is \(4(9 + 3)\). But wait, maybe the user's options are labeled differently. Wait, the user's image: the options are:

• \(3(12 + 9)\)

• \(2(18 + 12)\)

• \(4(9 + 3)\)

• \(6(30 + 2)\)

So by expanding each:

• \(3(12 + 9)=3\times12+3\times9 = 36 + 27=63

eq48(36 + 12)\)

• \(2(18 + 12)=2\times18+2\times12 = 36+24 = 60

eq48\)

• \(4(9 + 3)=4\times9+4\times3 = 36 + 12=48\) (matches \(36 + 12\))

• \(6(30 + 2)=6\times30+6\times2 = 180 + 12=192

eq48\)

So the correct option is \(4(9 + 3)\). But wait, in the user's image, maybe the options are presented as:

Option 1: \(3(12 + 9)\)

Option 2: \(2(18 + 12)\)

Option 3: \(4(9 + 3)\)

Option 4: \(6(30 + 2)\)

So the answer is \(4(9 + 3)\). But let's confirm again. \(36+12 = 48\), \(4(9 + 3)=4\times12 = 48\). Yes.

Answer:

\(4(9 + 3)\) (assuming the option with \(4(9 + 3)\) is one of the choices, and in the multiple - choice, the correct option is the one with \(4(9 + 3)\))