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# Factor with the distributive property

CCSS.Math:

## Video transcript

we're asked to apply the distributive property to factor out the greatest common factor we have 35 plus 50 is equal to so let me get my scratch pad out so we have 35 plus 50 is equal to now what's the greatest common factor of 35 and 50 so what's the largest whole number that's divisible into both of these well I could write 35 as let's see I could write that as 5 times 7 and I could write 50 as 5 times 10 and so we see 5 is the greatest common factor 7 and 10 don't have any factors in common so I could rewrite this I could write 35 as equal to 5 5 times 7 and I could rewrite 50 is equal to another color here I could rewrite 50 as 5 times 10 five times 10 and of course I'm adding them so I have plus right over here if I want I could put parentheses but order of operations would make me do the multiplication first anyway but now I want to factor out that greatest common factor I want to factor out I want to factor out the 5 so we're really doing right over here is I am unwinding the distributive property so if i factor out a 5 this is going to be equal to this is going to be equal to let's factor out the 5 5 times so you do 35 divided by 5 you're just left with the 7 you're just left with the 7 over here so you're just left with the 7 after you factor it out the 5 and over here you're just left with the 10 so 5 or 7 plus 7 plus 10 and we're done 35 plus 50 is equal to 5 times 7 plus 10 so let me let me now go and type that in so this is the same thing as 5 5 times 7 plus 10 and you know you factored out the greatest common factor because seven and ten don't have any factors in common anymore that they're called relatively prime they have no factors in common other than one so we could we could now check that let's do let's do a couple more of these apply the distributive property to factor out the greatest common factor so let's see if we can just do this one a little bit faster so see the largest number is divisible in both seventy-five and twenty I don't know let me try five so if I say five times so 75 divided by five let's see is going to be it's going to be fifteen is that right yeah because five times ten is fifty five times five is 25 yeah so it's 15 and I got that 15 by dividing 75 by 5 so 15 plus and then 20 divided by 5 would be 20 divided by 5 would be 4 15 plus 4 let's see did I do this right 15 and 4 don't have any factors in common and if I were to apply the distributive property here and if 5 times 15 is 75 5 times 4 is 20 yeah I'm feeling good about that got it right