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we're asked to rewrite the expression seven times open parenthesis 5 plus 11 close parenthesis as the sum of 35 and another whole number so really what they're asking us to do is just apply the distributive property we have 7 times the quantity 5 plus 11 now this is easy to calculate you could just say 5 plus 11 is 16 and then 16 times 7 is what that's 70 plus 42 which would be 112 but that's not what they're asking us to do they're not saying just calculate this you're saying express this as a sum of 35 and another whole number so let's apply the distributive property and let's see if we can get a sum of 35 and another whole number so 7 times 5 plus 11 that's the same thing as 7 times 5 plus plus 7 times 11 and you can see with this expression editor right over here it tells you it puts it kind of the nice math formatting for what it looks like for the computer so if we're distributing the 7 over the 5 and the 11 it's 7 times 5 plus 7 times 11 well 7 times 5 is 35 and 7 times 11 is 77 now have we done what they're asking us they said rewrite this expression as the sum of 35 and another whole number well we've done that we've written it as the sum of 35 and another whole number and we were able to do it do it using the distributive property so let's check to make sure that we got the right answer yes we did let's do one more of these rewrite the expression 12 plus 75 in the following form a times 4 plus C where a and C represent whole numbers now that this might look complex but they're really asking us to factor out an a factoring out an A out of this expression right over here seeing how much we can factor out so that one of these two numbers becomes a 12o becomes a 4 so let's think about how to do that if we look at these two numbers the greatest common divisor of 12 and 75 looks like it is 3 3 is definitely divisible into or both of them are divisible by 3 so you can write 12 12 is the same is three times four and 75 is the same thing as 3 times 3 times 25 now what we could do is we can essentially factor out we can factor out the 3 so this is where you could say we're undistributing in the 3 so that's the same thing 3 times 4 plus 3 times 25 that's the same thing as 3 that's the same thing as 3 times 4 plus 25 3 times 4 plus 25 and it looks like we've actually put it in the form that they want us to put it in where 3 is a and 4 is right there it's 4 and then C is 25 so we've put it in the right form let's check our answer we got it right