Expand and state your answer as a polynomial in standard form.left bracket, 5, x, squared, plus, y, to the power 4 , right bracket, squared(5x 2 +y 4 ) 2
Question
Expand and state your answer as a polynomial in standard form.left bracket, 5, x, squared, plus, y, to the power 4 , right bracket, squared(5x 2 +y 4 ) 2
Solution
To expand the given expression, we first need to understand that (a+b)^2 = a^2 + 2ab + b^2.
Here, a = 5x^2 and b = y^4.
So, (5x^2 + y^4)^2 = (5x^2)^2 + 2*(5x^2)*(y^4) + (y^4)^2.
Now, we simplify each term:
(5x^2)^2 = 25x^4, 2*(5x^2)(y^4) = 10x^2y^4, (y^4)^2 = y^8.
So, the expanded form of the given expression is 25x^4 + 10x^2*y^4 + y^8.
This is already in standard form, as the terms are written in descending order of degree.
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