hey it's kaylee now it's time to learn why we need the distributive property and why it's
so important in math with variables make sure you already know how to use the distributive
property over addition and subtraction before we get started with this one ready let's go
let's say we have an expression like this 3 times x plus 6 and i want you to evaluate it using order
of operations what would you do that's right we can rewrite it right here and we start with
what's inside our parentheses so we do our addition first what is x plus six
hm well we aren't given a given value for x so we can't really go any farther with this
but we can use the distributive property here to write out this in expanded form so if we have 3
times x plus 6 using the distributive property i take what's outside the parentheses and i multiply
to what's inside the parentheses so this will turn into 3 x plus three times six
and if i write this out in simplified form i'll have three x plus three times six is eighteen so
here we've just expanded our expression 3 times x plus 6 into 3 x plus 18 using the distributive
property nice this one says evaluate 7 times 4 minus x plus y using the distributive property
which is great that it says using the distributive property because i see some variables in here and
we know that order of operations won't work if we don't have given values so i'm going to rewrite my
expression first without my multiplication bullet i'm just going to cozy my 7 on up so it'll look
like 7 times 4 minus x plus y so now what do i do using the distributive property yeah i'm going to
distribute my 7 what's outside to what's inside the parentheses and what will that look like
seven times four minus seven x plus seven y and now i can simplify my multiplication here
7 times 4 is 28 minus 7x plus 7 y nice so do you see how the distributive property is important
when we have variables and order of operations won't help us we can rewrite our expression
in a way that might be easier for us to understand what's going on or like what the coefficients of
our variables will be nice let's do one more now this example says use the distributive property
to factor out the greatest common factor for the expression 45 minus 15 g so what does this mean
factor out what they're saying is they want us to take the expanded version
45 minus 15 g and write it in our factored form so that would be a number multiplied by
a number minus a number times g so we're kind of doing the reverse of what we have been doing
we've been taking the factored format and putting it into expanded format so what we need to do is
factor out the greatest common factor so our greatest common factor is going to be the gcf
of 45 and 15. do you remember how to find the gcf yeah we can use a prime factorization tree
so for 45 i start with my first prime number which is 3 and 3 times 15 here and then 15 can
still break into two more primes 3 and 5. now how about for 15 this will break into just 3 and 5.
now if i'm doing the gcf what do i do yeah i find the common ones so three and five
and three and five and then i multiply them together so the gcf is going to be equal to three
times five and that's equal to 15. so i'm factoring a 15 out of the expression so that
means that's this number here this is what's being factored out so that number becomes 15
and then i have my parentheses and if i'm factoring 15 out of 45 what am i doing
i'm dividing so 45 divided by 15 that'll leave us with a 3 here minus i'm factoring 15 out of 15 g
what is that so that would be like doing division here so 15 g divided by 15 my 15s will cancel out
and i'll be left with just one g which i can write as just g so this will just be g
so 15 all multiplied by 3 minus g is the factored form of 45 minus
15 g amazing job you have totally crushed this distributive property lesson are you ready to
practice on your own come back to the video if you need any help have fun and remember to always be
clever