{"status": "success", "data": {"description_md": "In the expansion of\n\n$$\\left(1 + x + x^2 + \\cdots + x^{27}\\right)\\left(1 + x + x^2 + \\cdots + x^{14}\\right)^2,$$<br>what is the coefficient of $x^{28}$?\n\n$\\mathrm{(A)}\\ 195\\qquad\\mathrm{(B)}\\ 196\\qquad\\mathrm{(C)}\\ 224\\qquad\\mathrm{(D)}\\ 378\\qquad\\mathrm{(E)}\\ 405$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>In the expansion of</p>&#10;<p><span class=\"katex--display\">\\left(1 + x + x^2 + \\cdots + x^{27}\\right)\\left(1 + x + x^2 + \\cdots + x^{14}\\right)^2,</span><br/>what is the coefficient of <span class=\"katex--inline\">x^{28}</span>?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ 195\\qquad\\mathrm{(B)}\\ 196\\qquad\\mathrm{(C)}\\ 224\\qquad\\mathrm{(D)}\\ 378\\qquad\\mathrm{(E)}\\ 405</span></p>&#10;<hr/>&#10;<p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2008 AMC 12A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12A_p20", "prev": "/problem/08_amc12A_p18"}}