{"id":19577,"date":"2022-12-01T10:00:50","date_gmt":"2022-12-01T04:30:50","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=19577"},"modified":"2022-12-02T09:19:12","modified_gmt":"2022-12-02T03:49:12","slug":"math-labs-activity-verify-identity-a3-b3-ab","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/math-labs-activity-verify-identity-a3-b3-ab\/","title":{"rendered":"Math Labs with Activity – Verify the Identity a\u00b3 + b\u00b3 =(a+b)(a\u00b2 -ab+b\u00b2)"},"content":{"rendered":"

Math Labs with Activity – Verify the Identity a\u00b3 + b\u00b3 =(a+b)(a\u00b2 -ab+b\u00b2)<\/strong><\/span><\/h2>\n

OBJECTIVE<\/strong><\/span><\/p>\n

To verify the identity a\u00b3 + b\u00b3 =(a+b)(a\u00b2 -ab+b\u00b2) using a set of unit cubes<\/p>\n

Materials Required<\/strong><\/span>
\nA set of 56 plastic cubes where each cube has dimensions (1 unit x 1 unit x 1 unit).<\/p>\n

Procedure<\/strong> <\/span>
\nWe shall verify the identity for a = 3 and b = 1.
\nStep 1:<\/strong> We shall make Arrangement 1 for 28 cubes.
\nThis arrangement will consist of two stacks as shown in Figures 4.1(a) and 4.1(b). The total volume of this arrangement of cubes is calculated (see the calculations).
\n\"Math
\nStep 2:<\/strong> We shall now make Arrangement 2 for the remaining 28 cubes.
\nThis arrangement will consist of two stacks as shown in the Figures 4.2(a) and 4.2(b). The total volume of this arrangement of cubes is calculated (see the calculations).
\n\"Math<\/p>\n

Observations<\/strong><\/span>
\nSince the two arrangements have equal number of cubes (each arrangement has 28 cubes) and all the cubes have the same volume (1 cubic unit), the total volume in both the cases must be the same.<\/p>\n

Calculations<\/strong><\/span><\/p>\n

    \n
  1. Volume of Arrangement 1<\/strong>
    \nVolume of the stack in Figure 4.1(a) = a\u00b3.
    \nVolume of the stack in Figure 4.1(b) = b\u00b3.
    \ntotal volume of the arrangement=(a\u00b3 + b\u00b3).<\/li>\n
  2. Volume of Arrangement 2<\/strong>
    \nVolume of the stack in Figure 4.2(a) =(a+b)(a -b)a.
    \nVolume of the stack in Figure 4.2(b) = (a+b)b\u00b2.
    \ntotal volume of the arrangement = (a+b)(a -b)a + (a+b)b\u00b2
    \n=(a+b){(a-b)a+b\u00b2} =(a+b)(a\u00b2 -ab +b\u00b2).
    \nSince the total volume in the two arrangements is the same, therefore a\u00b3 + b\u00b3 =(a+b)(a\u00b2 -ab+b\u00b2).<\/li>\n<\/ol>\n

    Result<\/strong> <\/span>
    \nIt is verified that a\u00b3 + b\u00b3 =(a+b)(a\u00b2 -ab+b\u00b2).<\/p>\n

    Remarks:<\/strong> The students must try to verify this identity for other values of a and b by taking required number of cubes and arranging them suitably.<\/p>\n

    Math Labs with Activity<\/a>Math Labs<\/a>Math Lab Manual<\/a>Science Labs<\/a>Science Practical Skills<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

    Math Labs with Activity – Verify the Identity a\u00b3 + b\u00b3 =(a+b)(a\u00b2 -ab+b\u00b2) OBJECTIVE To verify the identity a\u00b3 + b\u00b3 =(a+b)(a\u00b2 -ab+b\u00b2) using a set of unit cubes Materials Required A set of 56 plastic cubes where each cube has dimensions (1 unit x 1 unit x 1 unit). Procedure We shall verify the […]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[6805],"tags":[],"yoast_head":"\nMath Labs with Activity - Verify the Identity a\u00b3 + b\u00b3 =(a+b)(a\u00b2 -ab+b\u00b2) - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/math-labs-activity-verify-identity-a3-b3-ab\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Math Labs with Activity - Verify the Identity a\u00b3 + b\u00b3 =(a+b)(a\u00b2 -ab+b\u00b2)\" \/>\n<meta property=\"og:description\" content=\"Math Labs with Activity – Verify the Identity a\u00b3 + b\u00b3 =(a+b)(a\u00b2 -ab+b\u00b2) OBJECTIVE To verify the identity a\u00b3 + b\u00b3 =(a+b)(a\u00b2 -ab+b\u00b2) using a set of unit cubes Materials Required A set of 56 plastic cubes where each cube has dimensions (1 unit x 1 unit x 1 unit). 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