Answer:
8 + 12y² + 6x² +
Step-by-step explanation:
This can be expanded using the binomial theorem or by multiplying the factors.
In case you are not aware of the theorem, will do multiplication.
Given
(2x² + y²)³ = (2x² + y²)(2x²+ y²)(2x² + y²)
Expanding the second pair of factors
Each term in the second factor is multiplied by each term in the first factor, that is
2x²(2x² + y²) + y²(2x² + y²) ← distribute both parenthesis
= 4 + 2x²y² + 2x²y² + ← collect like terms
= 4 + 4x²y² +
Now multiply this by the remaining factor (2x² + y²)
(2x² + y²)(4 + 4x²y² + )
= 2x²(4 + 4x²y² + ) + y²(4 + 4x²y² + ) ← distribute both parenthesis
= 8+ 8y² + 2x² + 4y² + 4x² + ← collect like terms
= 8 + 12y² + 6x² +