Question

question
combine like terms.
$1 - 2x^2 - x^2 + 2y^2$

Explanation:

Step1: Identify like terms

The terms with \(x^2\) are \(-2x^2\) and \(-x^2\). The constant term is \(1\), and the term with \(y^2\) is \(2y^2\).

Step2: Combine \(x^2\) terms

Combine \(-2x^2 - x^2\). Using the rule of combining like terms (add coefficients), we have \(-2x^2 - x^2 = (-2 - 1)x^2 = -3x^2\).

Step3: Rewrite the expression

Substitute the combined \(x^2\) term back into the original expression. So the expression becomes \(1 - 3x^2 + 2y^2\) (or \(1 + 2y^2 - 3x^2\) as the order of terms doesn't matter for addition).

Answer:

\(1 - 3x^2 + 2y^2\) (or equivalent form like \(1 + 2y^2 - 3x^2\))