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Here, multiply each term in the first bracket by each term in the second bracket; do not forget the two middle products.","highlights":[{"text":"Write $(3 - \\sqrt{2})^2$ in the form $a + b\\sqrt{2}$, where $a$ and $b$ are integers.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"(3-\\sqrt{2})^2=(3-\\sqrt{2})(3-\\sqrt{2})"},{"latex":"(3-\\sqrt{2})(3-\\sqrt{2})=9-3\\sqrt{2}-3\\sqrt{2}+2"}]},"order":1,"title":"Expand every product","description":"Write all four products before collecting terms. This full expansion earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"9+2=11"},{"latex":"9-3\\sqrt{2}-3\\sqrt{2}+2=11-6\\sqrt{2}"}]},"order":2,"title":"Collect like terms","description":"Combine the ordinary numbers, then combine the two square-root terms. 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