# SOLUTION: Factor: Factor the product of polynomial 4r^2-20ry+25y^2 Please show me steps by steps to get the answer. Thanks

Algebra ->  Algebra  -> Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Factor: Factor the product of polynomial 4r^2-20ry+25y^2 Please show me steps by steps to get the answer. Thanks      Log On

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 Question 463239: Factor: Factor the product of polynomial 4r^2-20ry+25y^2 Please show me steps by steps to get the answer. ThanksAnswer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website!``` 4r²-20ry+25y² Multiply the 4 by the 25 ignoring signs. Get 100 Write down all the ways to have two positive integers which have product 100, starting with 100*1 100*1 50*2 25*4 20*5 10*10 Since the last sign in 4r²-20ry+25y² is +, ADD them, and place the SUM out beside that: 100*1 100+1=101 50*2 50+2=52 25*4 25+4=29 20*5 20+5=25 10*10 10+10=20 Now, again ignoring signs, we find in that list of sums the coefficient of the middle term in 4r²-20ry+25y² So we replace the number 20 by 10+10 4r²-20ry+25y² 4r²-(10+10)ry+25y² Then we distribute to remove the parentheses: 4r²-10ry-10ry+25y² Factor the first two terms 4r²-10ry by taking out the greatest common factor, getting 2r(2r-5y) Factor the last two terms -10ry+25y² by taking out the greatest common factor, -5y, getting -5y(2r-5y) So we have 2r(2r-5y)-5y(2r-5y) Notice that there is a common factor, (2r-5y) 2r(2r-5y)-5y(2r-5y) which we can factor out leaving the 2r and the -5y to put in parentheses: (2r-5y)(2r-5y) But since the two factors are the same, we can write it simply as (2r-5y)² Edwin```