Question

Evaluate (2x^2+y^2)3

Answer 1

8
`x^(6)` + 12
`x^(4)`y² + 6x²
`y^(4)` +
`y^(6)`

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
`x^(4)` + 2x²y² + 2x²y² +
`y^(4)` ← collect like terms

= 4
`x^(4)` + 4x²y² +
`y^(4)`

Now multiply this by the remaining factor (2x² + y²)

(2x² + y²)(4
`x^(4)` + 4x²y² +
`y^(4)`)

= 2x²(4
`x^(4)` + 4x²y² +
`y^(4)`) + y²(4
`x^(4)` + 4x²y² +
`y^(4)`) ← distribute both parenthesis

= 8
`x^(6)`+ 8
`x^(4)`y² + 2x²
`y^(4)` + 4
`x^(4)`y² + 4x²
`y^(4)` +
`y^(6)` ← collect like terms

= 8
`x^(6)` + 12
`x^(4)`y² + 6x²
`y^(4)` +
`y^(6)`