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(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca): find the missing part

This type of question, asked 6 times: 14 Jul 2023 S1, 17 Jul 2023 S3, 18 Jul 2023 S2, 18 Jul 2023 S4, 20 Jul 2023 S2, 26 Jul 2023 S2. All 6 questions below, oldest first.

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  1. Question 1

    14 Jul 2023 S1

    72
    If (a+b+c)=16(a + b + c) = 16, and (a2+b2+c2)=90(a^2 + b^2 + c^2) = 90, find the value of (ab+bc+ca)(ab + bc + ca).

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  2. Question 2

    17 Jul 2023 S3

    52
    What is the value of the given expression? (a+b+c)2−a2−b2−c2(a + b + c)^2 - a^2 - b^2 - c^2

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  3. Question 3

    18 Jul 2023 S2

    68
    If (a+b+c)=19(a + b + c) = 19, and (a2+b2+c2)=155(a^2 + b^2 + c^2) = 155, find the value of (a−b)2+(b−c)2+(c−a)2(a - b)^2 + (b - c)^2 + (c - a)^2.

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  4. Question 4

    18 Jul 2023 S4

    52
    If a+b+c=6a + b + c = 6 and a2+b2+c2=14a^2 + b^2 + c^2 = 14, then what is the value of (a−b)2+(b−c)2+(c−a)2(a - b)^2 + (b - c)^2 + (c - a)^2?

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  5. Question 5

    20 Jul 2023 S2

    67
    If x + y + z = 4 and x2+y2+z2=12x^2 + y^2 + z^2 = 12, then find xy + yz + xz.

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  6. Question 6

    26 Jul 2023 S2

    63
    If (a+b+c)=13(a + b + c) = 13, and (ab+bc+ca)=54(ab + bc + ca) = 54, find the value of (a2+b2+c2)(a^2 + b^2 + c^2).

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