Show that if 2(a2 + b2) = (a + b)2, then a = b. from Mathemati
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    Polynomials

    Multiple Choice QuestionsShort Answer Type

    161.

    Simplify: (x + y)3 - (x - y)3 - 6y(x2 - y2)    

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    162. If x2 + px + q = (x + a)(x + b), then factorise x2 + pxy + qy2.
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    163. Prove that: (a + b)3 + (b + c)3 + (c + a)3 - 3(a + b)(b + c)(c + a) = 2(a3 + b3+ c3 - 3abc).
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    164. Evaluate using suitable identify: (999)3.
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    165. Multiply 9x2 + 25y2 + 15xy + 12x -20y + 16 by 3x - 5y - 4 using suitable identity.
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    166. Show that if a + b is not zero, then the equation a(x - a) = 2ab - b(x - b) has a solution x = a + b.
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    167. Show that if 2(a2 + b2) = (a + b)2, then a = b.

    2(a2 + b2) = (a + b)2
    ⇒ 2a2 + 2b2 = a2 + b2 + 2ab
    ⇒ a2 + b2 - 2ab = 0
    ⇒    (a - b)2 = 0
    ⇒    a - b = 0
    ⇒    a = b.

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    168.

    Factorise each of the following:

    a4 - b4    (b)a4 - 16b4

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    169.

    Factorise each of the following:

    a4 - 16b4 

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    170.

    Factorise each of the following:

    a2 - (b - c)2

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