Share
Expand (3x^5 + y)^2 Polynomial in Standard Form
Published on March 24, 2026
Algebra
Expand the binomial (3x^5 + y)^2 using the perfect square formula (a+b)^2 = a^2 + 2ab + b^2 to get the polynomial 9x^10 + 6x^5y + y^2 in standard form.
Question
Answer
The problem asks to expand the expression
Step 1: Recognize the form of the expression.
The expression is in the form of a perfect square binomial,
The expression is in the form of a perfect square binomial,
Step 2: Apply the formula for squaring a binomial.
The formula is:
The formula is:
Step 3: Substitute
Step 4: Simplify each term.
For the first term,
For the first term,
For the second term,
For the third term,
Step 5: Combine the simplified terms.
Step 6: State the answer in standard form.
A polynomial in standard form is typically written with terms arranged in descending order of the degree of the terms. In this case, the degrees are:
A polynomial in standard form is typically written with terms arranged in descending order of the degree of the terms. In this case, the degrees are:
- ā¢
: degree (considering as the primary variable, or total degree ) - ā¢
: total degree - ā¢
: total degree
Arranging by total degree in descending order:
The resulting polynomial is already in standard form with respect to the total degree of the terms.
The resulting polynomial is already in standard form with respect to the total degree of the terms.
The expanded form in standard form is:
The final answer is: