Question

State your answer as a polynomial in standard form (2x⁴+y)²

Answer 1

To expand (2x⁴ + y)² into a polynomial in standard form, apply the binomial expansion to get 4x⁴² + 4x⁴y + y², which simplifies to 4x⁸ + 4x⁴y + y².

Step-by-step explanation:

To express (2x⁴ + y)² as a polynomial in standard form, we first apply the binomial expansion formula.

The expansion is (a + b)² = a² + 2ab + b², where a = 2x⁴ and b = y.

Plugging in the values we get:

• (2x⁴)² = 4x⁴²
• 2 × 2x⁴ × y = 4x⁴y
• y²

Adding these terms together:

4x⁴² + 4x⁴y + y²

Now we write down the exponents in descending order to get the polynomial in standard form:

4x⁸ + 4x⁴y + y²

This is the expanded form of the given expression in standard form.