Which expression uses the greatest common factor and the distributive property to rewrite the sum 42 + 72? 6(7 + 12) 7(6 + 9) 12(3 + 6) 2(40 + 70) im doing a test need answer asap

The answer is 6(7 + 12) ⇒ 1st answer

Step-by-step explanation:

* Lets explain how to solve the problem

- Factors are the numbers you multiply together to get another number

- Ex: 4 × 5 = 20 ⇒ 4 and 5 are the factors of 20

- Factors of a number n are the numbers that can multiplied together

 to give the number n

- Ex: The factors of 6 are 1 , 2 , 3 , 6 because 1 × 6 = 6 and 2 × 3 = 6

- The distributive property lets you multiply a sum by multiplying each

  term separately and then add the products

- Ex: a(b + c) = ab + ac

* Lets solve the problem

- We want to find the greatest common factor in 42 + 72

∵ 42 = 1 × 42 , 2 × 21 , 3 × 14 , 6 × 7

∴ The factors of 42 are 1 , 2 , 3 , 6 , 7 , 14 , 21 , 42

∵ 71 = 1 × 72 , 2 × 36 , 3 × 24 , 4 × 18 , 6 × 12 , 8 × 9

∴ The factors of 72 are 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 18 , 24 , 36 , 72

- The common factors between 42 and 72 are the bold numbers

∵ The common factors between 42 and 72 are 1 , 2 , 3 , 6

∵ The greatest one of them is 6

∴ The greatest common factor of 42 and 72 is 6

- In the distributive property we have a number multiplying by a sum

 of two numbers

∵ 42 ÷ 6 = 7 and 72 ÷ 6 = 12

- We can write 42 + 72 as 6 × 7 + 6 × 12 and take 6 as a common factor

∵ 42 + 72 = 6 × 7 + 6 × 12

- Take 6 as a common factor

∴ 42 + 72 = 6(7 + 12)

answer: x=60