Answer :
Let's simplify and rewrite the expression [tex]\( y = 1 + 2x^6 - 4x^2 - 2x^6 \)[/tex] into standard form.
1. Identify and Combine Like Terms:
- The terms [tex]\( 2x^6 \)[/tex] and [tex]\( -2x^6 \)[/tex] can be combined because they are like terms. When you add these together:
[tex]\[
2x^6 - 2x^6 = 0
\][/tex]
- So, these terms cancel each other out.
2. Rewrite the Expression:
- After combining like terms, the equation now simplifies to:
[tex]\[
y = 1 - 4x^2
\][/tex]
3. Standard Form of a Polynomial:
- A polynomial is typically written in standard form as [tex]\( y = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0 \)[/tex], where the powers of [tex]\( x \)[/tex] are written in descending order.
- In this case, the expression is already in standard form. The term [tex]\( -4x^2 \)[/tex] comes first, followed by the constant [tex]\( 1 \)[/tex].
Thus, the standard form of the equation is:
[tex]\[
y = -4x^2 + 1
\][/tex]
1. Identify and Combine Like Terms:
- The terms [tex]\( 2x^6 \)[/tex] and [tex]\( -2x^6 \)[/tex] can be combined because they are like terms. When you add these together:
[tex]\[
2x^6 - 2x^6 = 0
\][/tex]
- So, these terms cancel each other out.
2. Rewrite the Expression:
- After combining like terms, the equation now simplifies to:
[tex]\[
y = 1 - 4x^2
\][/tex]
3. Standard Form of a Polynomial:
- A polynomial is typically written in standard form as [tex]\( y = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0 \)[/tex], where the powers of [tex]\( x \)[/tex] are written in descending order.
- In this case, the expression is already in standard form. The term [tex]\( -4x^2 \)[/tex] comes first, followed by the constant [tex]\( 1 \)[/tex].
Thus, the standard form of the equation is:
[tex]\[
y = -4x^2 + 1
\][/tex]
