random kumon homework

How do i solve these two questions and why are their solving processes different (i think?)
1. 3x²(x-2y)²+ 3y²(x+2y)²
2. 4x(x+2y)² + 3y²(x+2y)
Are their solving processes different because of the exponent thingy (the ones in red because when i was doing my kumon i thought something was up with it and might be why i got it wrong)
but thats all i dont even know what this is i think its algebra 1 but idk.

  • Mathe Mathe

    What are the questions?

    • Ruklvr Ruklvr

      1. 3x²(x-2y)²+ 3y²(x+2y)² 2. 4x(x+2y)² + 3y²(x+2y) how do you like factorize them out thats what I'm doing in kumon i think

1 Answer

1. Are you sure there is no typo? I don't think it can be factored. The correct form might be $3x²(x+2y)²+ 3y²(x+2y)²$. in that case

\[3x²(x+2y)²+ 3y²(x+2y)²=3(x+2y)^2(x^2+y^2).\]

2. The second expression can be factored as follows: 
\[4x(x+2y)^2+ 3y^2(x+2y)=(x+2y)[4x(x+2y)+3y^2]=(x+2y)(4x^2+8xy+3y^2)\]
\[=(x+2y) (2x+2y -y)(2x+2y+y)\]
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