{"id":19588,"date":"2022-12-01T10:00:43","date_gmt":"2022-12-01T04:30:43","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=19588"},"modified":"2022-12-02T09:18:58","modified_gmt":"2022-12-02T03:48:58","slug":"math-labs-activity-verify-identity-a3-b3-ab-a2-ab-b2","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/math-labs-activity-verify-identity-a3-b3-ab-a2-ab-b2\/","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 identify 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 53 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 26 cubes.
\nTake 27 cubes and place them to form a stack consisting of 9 columns, each column having 3 cubes [see Figure 5.1(a)]. From this stack remove one cube [see Figure 5.1(b)] to form a stack consisting of 26 cubes as shown in Figure 5.1(c). The stack in Figure 5.1(c) forms Arrangement 1. The total volume of this arrangement of cubes is calculated (see the calculations).
\n\"Math
\nStep 2:<\/strong> We shall make Arrangement 2 for 26 cubes.
\nThis arrangement consists of three stacks\u2014the first stack [shown in Figure 5.2(a)] consists of 9 columns of two cubes each, the second stack [shown in Figure 5.2(b)] consists of two rows of three cubes each, and the third stack consists of 1 row of 2 cubes.
\nThe 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 26 cubes) and all the cubes have the same volume (1 cubic unit), the total volumes in both the arrangements must be equal.<\/p>\n

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

    \n
  1. Volume of Arrangement 1
    \nVolume of the stack in Figure 5.1(a) = a\u00b3.
    \nVolume of the stack in Figure 5.1(b) =b\u00b3.
    \n=volume of Arrangement 1 volume of the stack in Figure 5.1(c)
    \n= volume of the stack in Figure 5.1(a)
    \n=volume of the stack in Figure 5.1(b) = a\u00b3-b\u00b3.<\/li>\n
  2. Volume of Arrangement 2
    \nVolume of the stack in Figure 5.2(a)=(a-b)a\u00b2.
    \nVolume of the stack in Figure 5.2(b) =(a-b)ab.
    \nVolume of the stack in Figure 5.2(c) = (a-b)b\u00b2.
    \nvolume of Arrangement 2 = (a-b)a\u00b2 + (a -b)ab + (a -b)b\u00b2.
    \n=(a-b)(a\u00b2 + ab+b\u00b2).
    \nSince the total volume in the two arrangements must be the same, therefore
    \na\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 identify a\u00b3 – b\u00b3 =(a-b)(a\u00b2 + ab+b\u00b2) using a set of unit cubes Materials Required A set of 53 plastic cubes where each cube has dimensions (1 unit x 1 unit x 1 unit). Procedure We shall […]<\/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-a2-ab-b2\/\" \/>\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 identify a\u00b3 – b\u00b3 =(a-b)(a\u00b2 + ab+b\u00b2) using a set of unit cubes Materials Required A set of 53 plastic cubes where each cube has dimensions (1 unit x 1 unit x 1 unit). 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