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Class 9
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Math
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Algebraic Manipulation
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Formulas / Equations

Algebraic Manipulation

Formulas / Equations

Math

  • a2−b2=(a+b)(a−b)a^2 - b^2 = (a+b)(a-b)

  • (a+b)2+(a−b)2=2(a2+b2)(a+b)^2+(a-b)^2 = 2(a^2+b^2)

  • (a+b)2−(a−b)2=4ab(a+b)^2-(a-b)^2 = 4ab

  • (a+b+c)2=a2+b2+c2+2ab+2bc+2ca(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

  • (a+b)3=a3+b3+3ab(a+b)(a+b)^3 = a^3 + b^3 + 3ab(a+b)

  • (a−b)3=a3−b3−3ab(a−b)(a-b)^3 = a^3 - b^3 - 3ab(a-b)

  • a3+b3=(a+b)(a2−ab+b2)a^3 + b^3 = (a+b)(a^2 - ab + b^2)

  • a3−b3=(a−b)(a2+ab+b3)a^3-b^3 = (a-b)(a^2+ab+b^3)

  • L.C.M =\text{L.C.M =}

    (Product of common factors)\text{(Product of common factors)}

                                                ×\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\times

    (Product of non-common factors)\text{(Product of non-common factors)}

  • H.C.F×L.C.M=p(x)×q(x)\text{H.C.F} \times \text{L.C.M} = p(x)\times q(x)