Question

expand and state your answer as a polynomial in standard form.
\\((5x^2 + y^2)^2\\)

Explanation:

Step1: Apply square of sum formula

Recall $(a+b)^2 = a^2 + 2ab + b^2$, let $a=5x^2$, $b=y^2$.
$$(5x^2 + y^2)^2 = (5x^2)^2 + 2(5x^2)(y^2) + (y^2)^2$$

Step2: Simplify each term

Calculate the powers and products:
$$(5x^2)^2 = 25x^4, \quad 2(5x^2)(y^2)=10x^2y^2, \quad (y^2)^2=y^4$$

Step3: Combine terms in standard form

Arrange terms by descending degree of $x$ (or total degree):
$$25x^4 + 10x^2y^2 + y^4$$

Answer:

$25x^4 + 10x^2y^2 + y^4$