1. **State the problem:** Simplify the expression $ax^2 + bx^2 - bx - ax + a + b$. 2. **Group like terms:** Group terms with $x^2$, terms with $x$, and constant terms: $$ (ax^2 + bx^2) + (-bx - ax) + (a + b) $$ 3. **Factor each group:** - For $x^2$ terms: $ax^2 + bx^2 = (a + b)x^2$ - For $x$ terms: $-bx - ax = -(b + a)x = -(a + b)x$ - Constants: $a + b$ 4. **Rewrite the expression:** $$ (a + b)x^2 - (a + b)x + (a + b) $$ 5. **Factor out the common factor $(a + b)$:** $$ (a + b)(x^2 - x + 1) $$ 6. **Final answer:** The simplified form is $$ (a + b)(x^2 - x + 1) $$ This shows the expression factored by grouping and common factors.