Answer:
8
+ 12
y² + 6x²
+
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
+ 8
y² + 2x²
+ 4
y² + 4x²
+
← collect like terms
= 8
+ 12
y² + 6x²
+