Question

simplify.
$(4x^4 + y^4)^2$

Explanation:

Step1: Recall the square of a binomial formula

The formula for \((a + b)^2\) is \(a^2 + 2ab + b^2\). Here, \(a = 4x^4\) and \(b = y^4\).

Step2: Apply the formula to \((4x^4 + y^4)^2\)

First, calculate \(a^2=(4x^4)^2 = 4^2\times(x^4)^2=16x^8\).
Then, calculate \(2ab = 2\times(4x^4)\times(y^4)=8x^4y^4\).
Next, calculate \(b^2=(y^4)^2 = y^8\).

Step3: Combine the terms

Add the three terms together: \(16x^8+8x^4y^4 + y^8\).

Answer:

\(16x^8 + 8x^4y^4 + y^8\)