Question

factor 9x ^2 - 30xy + 25y^ 2

Answer 1

Notice how 9x^2 = (3x)^2 and 25y^2 = (5y)^2


Also, -30xy = -2*3x*5y


So this means we have a perfect square


\[\large (a-b)^2=a^2-2ab+b^2\] where in this case a = 3x and b = 5y


So \[\large (3x-5y)^2=(3x)^2-2(3x)(5y)+(5y)^2\]


\[\large (3x-5y)^2=9x^2-30xy+25y^2\]

Answer 2

\[9x^2-15xy-15xy+25y^2\]
\[3x(3x-5y)-5y(3x-5y)\]
\[(3x-5y)(3x-5y)=(3x-5y)^2\]