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# Multiplying binomials by polynomials

CCSS.Math:

## Video transcript

we are multiplying 10 a minus 3 by the entire polynomial 5a squared plus 7a minus 1 so to do this we can just do the distributive property we can distribute this entire polynomial this entire trinomial times each of these terms we could have 5a squared plus 7a minus 1 times x 10 a times 10 a and then 5 a squared plus 7a minus 1 times negative 3 so let's just do that so if we have so let me just write it out so we could have 5 let me write it this way 10 a 10 we could have 10 a times 5a squared plus 7a minus 1 that's that right over here and then we can have minus 3 times 5a squared plus 7a minus 1 and that is this distribution right over here and then we can simplify it 10 a times 5a squared 10 times 5 is 50 a times a squared is a to the third 10 times 7 is 70 a times a is a squared 10 a times negative 1 is negative 10 a then we distribute this negative 3 times all of this negative 3 times 5a squared is negative 15a squared negative 3 times 7 a is negative 21 a negative 3 times negative 1 is positive 3 and now we can try to merge like terms this is the only a to the third term here so this is 50 a to the third I'll just rewrite it now we have 2a squared terms we have 70 a squared minus 15 or negative 15 a squared so we can add these two terms seventy of something minus 15 of that something is going to be 55 of that something so plus plus 55 a squared and then we also have 2a terms so we have this negative 10a and then we have this negative 21 a so if we go negative 10 minus 21 that is negative 31 that is Nega 5:31 a so that is negative 31 a and then well we want to put your negative 31 a and then finally we only have one constant term over here we have this positive 3 so plus 3 and we are done