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Factorize 5y^2- 125z^2​

User Zack Bartel
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1 Answer

18 votes
18 votes

Answer:


5\left(y+5z\right)\left(y-5z\right)

Explanation:


\mathrm{The \;given \;equation \;is \; 5y^2-125z^2}


\mathrm{Factor\:out\:common\:term\:}5:\quad 5\left(y^2-25z^2\right)\\\\= 5\left(y^2-25z^2\right)


\left y^2-25z^2\right

25z^2 = \left(5z\right)^2
==>
\left y^2-25z^2\right = y^2-\left(5z\right)^2


\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)

y^2-\left(5z\right)^2=\left(y+5z\right)\left(y-5z\right)

So the factored expression is

5\left(y+5z\right)\left(y-5z\right)

User Jawsware
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2.7k points