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Chapter 5: Problem 50

Find each product. $$\left(2 x^{2}+y^{2}\right)^{2}$$

Short Answer

Expert verified
The product \((2 x^{2}+y^{2})^2\) simplifies to \(4x^4 + 4x^2*y^2 + y^4\).

Step by step solution

01

Identify a and b

In our expression \((2x^2 + y^2)^2\), identify \(a = 2x^2\) and \(b = y^2\)
02

Apply the Binomial Theorem

Applying the binomial theorem to our expression, we get \((2x^2 + y^2)^2 = (2x^2)^2 + 2*2x^2*y^2 + (y^2)^2\)
03

Simplify the Equation

Simplify to obtain the final answer: \(4x^4 + 4x^2*y^2 + y^4\)

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