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

User Willhess
by
3.6k points

1 Answer

4 votes

Answer:

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)

User Woodchuck
by
4.2k points