Question 434771: Ello,
factoring the problem b^2+16b+64
thank you
makiki
Answer by tinbar(133)   (Show Source):
You can put this solution on YOUR website! you basically want two numbers x and y to satisfy the following conditions x*y=64 and x+y=16. to see why this is, assume we have factored our equation b^2+16b+64 into (b+x)(b+y). Let's expand and see what happens with this x and y. we get, upon expansion, (b^2)+(b*y)+(b*x)+(x*y). now the two middle terms both have b as a common factor, so (b*y)+(b*x) = (b*(y+x)). so now we can rewrite the entire expansion as (b^2)+(b*(y+x))+(x*y). Now compare this to the equation b^2+16b+64. the first term, b^2, is already satisfied, the second term in your equation says 16*b, in our expansion we have (b*(y+x)) so then (y+x)=16, and also, in your equation the third term is 64, in our expansion we have (x*y), so (x*y)=64
You can either guess what x and y is, or use a system of linear equations. X=8 and Y=8 in this case. If you would like to know how to have solved x and y without guessing, reply back and i'll explain
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