Question

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

Answer 1

Answer:

8$x^{6}$ + 12$x^{4}$y² + 6x²$y^{4}$ + $y^{6}$

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$x^{4}$ + 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$y^{4}$ + $y^{6}$

Answer 2

The Answer is 6x2+3y2