Multiplication of Monomials

Chapter 8 Class 8 Algebraic Expressions and Identities
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Ex 8.2, 3 Complete the table of products. For 2x 2π₯Γ2π₯ = 2Γπ₯Γ2Γπ₯ = (2Γ2)Γ(π₯Γπ₯) = 4 Γπ₯^2 = 4π₯^2 Ex 8.2, 3 Complete the table of products. For 2x 2π₯Γβ5π¦ = 2Γπ₯Γβ5Γπ¦ = (2Γβ5)Γπ₯Γπ¦ = β10Γπ₯Γπ¦ = β10π₯π¦ Ex 8.2, 3 Complete the table of products. For 2x 2π₯Γ3π₯^2 = 2Γπ₯Γ3Γπ₯^2 = (2Γ3)Γ(π₯Γπ₯^2 ) = 6Γπ₯^3 = 6π₯^3 Ex 8.2, 3 Complete the table of products. For 2x 2π₯Γβ4π₯π¦ = 2Γπ₯Γβ4Γπ₯Γy = (2Γβ4)Γ(π₯Γπ₯)Γπ¦ = β8Γπ₯^2Γπ¦ = β8π₯^2 π¦ Ex 8.2, 3 Complete the table of products. For 2x 2π₯Γ7π₯^2 π¦ = 2Γπ₯Γ7Γπ₯^2Γy = (2Γ7)Γ(π₯Γπ₯^2 )Γπ¦ = 14Γπ₯^3Γπ¦ = 14π₯^3 π¦ Ex 8.2, 3 Complete the table of products. For 2x 2π₯Γβ9π₯^2 π¦^2 = 2Γπ₯Γβ9Γπ₯^2Γy^2 = (2Γβ9)Γ(π₯Γπ₯^2 )Γπ¦^2 = β18Γπ₯^3Γπ¦^2 = β18π₯^3 π¦^2 Ex 8.2, 3 Complete the table of products. For β5y (β5π¦)Γ2π₯ = β5Γπ¦Γ2Γπ₯ = (β5Γ2)Γ(π¦Γπ₯) = β10Γπ₯π¦ = β10π₯π¦ Ex 8.2, 3 Complete the table of products. For β5y (β5π¦)Γ(β5π¦) = β5Γπ¦Γβ5Γπ¦ = (β5Γβ5)Γ(π¦Γπ¦) = 25Γπ¦^2 = 25π¦^2 Ex 8.2, 3 Complete the table of products. For β5y (β5π¦)Γ3π₯^2 = β5Γπ¦Γβ5Γπ₯^2 = (β5Γ3)Γπ¦Γπ₯^2 = β15Γπ₯^2Γπ¦ = β15π₯^2 π¦ Ex 8.2, 3 Complete the table of products. For β5y (β5π¦)Γ(β4π₯π¦) = β5Γπ¦Γβ4Γπ₯Γπ¦ = (β5Γβ4)Γπ¦Γπ¦Γπ₯ = 20Γπ¦^2Γπ₯ = 20π¦^2 π₯ Ex 8.2, 3 Complete the table of products. For β5y (β5π¦)Γ7π₯^2 π¦ = β5Γπ¦Γ7Γπ₯^2Γπ¦ = (β5Γ7)Γ(π¦Γπ¦)Γπ₯^2 = β35Γπ¦^2Γπ₯^2 = β35π¦^2 π₯^2 Ex 8.2, 3 Complete the table of products. For β5y (β5π¦)Γ(β9π₯^2 π¦^2 ) = β5Γπ¦Γ(β9)Γπ₯^2Γπ¦^2 = (β5Γβ9)Γπ₯^2Γ(π¦Γπ¦^2 ) = 45Γπ₯^2Γπ¦^3 = 45π₯^2 π¦^3 Ex 8.2, 3 Complete the table of products. For 3x2 3π₯^2Γ2π₯ = 5Γπ₯^2Γ2Γπ₯ = (3Γ2)Γ(π₯^2Γπ₯) = 6Γπ₯^3 = 6π₯^3 Ex 8.2, 3 Complete the table of products. For 3x2 3π₯^2Γ(β5π¦) = 3Γπ₯^2Γβ5Γπ¦ = (3Γβ5)Γπ₯^2Γπ¦ = β15π₯^2 π¦^2 Ex 8.2, 3 Complete the table of products. For 3x2 3π₯^2Γ3π₯^2 = 3Γπ₯^2Γ3Γπ₯^2 = (3Γ3)Γ(π₯^2Γπ₯^2 ) = 9Γπ₯^4 = 9π₯^4 Ex 8.2, 3 Complete the table of products. For 3x2 3π₯^2Γ(β4π₯π¦) = 3Γπ₯^2Γβ4Γπ₯Γπ¦ = (3Γβ4)Γ(π₯^2Γπ₯)Γπ¦ = β12Γπ₯^3Γπ¦ = β12π₯^3 π¦ Note: π₯π Γπ₯π = π₯^(π + π) Ex 8.2, 3 Complete the table of products. For 3x2 3π₯^2Γ7π₯^2 π¦ = 3Γπ₯^2Γ7Γπ₯^2Γπ¦ = (3Γ7)Γ(π₯^2Γπ₯^2 )Γπ¦ = 21Γπ₯^4Γπ¦ = 21π₯^4 π¦ Ex 8.2, 3 Complete the table of products. For 3x2 3π₯^2Γ(β9π₯^2 π¦^2) = 3Γπ₯^2Γ7Γπ₯^2Γπ¦ = (3Γβ9)Γ(π₯^2Γπ₯^2 )Γπ¦^2 = β27Γπ₯^4Γπ¦^2 = β27π₯^4 π¦^2 Ex 8.2, 3 Complete the table of products. For βπππ (β4π₯π¦)Γ2π₯ = β4Γπ₯Γπ¦Γ2Γπ₯ = (β4Γ2)Γ(π₯Γπ₯)Γπ¦ = β8Γπ₯^2Γπ¦ = β8π₯^2 π¦ Ex 8.2, 3 Complete the table of products. For βπππ (β4π₯π¦)Γ(β5π¦) = β4Γπ₯Γπ¦Γβ5Γπ¦ = (β4Γβ5)Γπ₯Γ(π¦Γπ¦) = 20Γπ₯Γπ¦^2 = 20π₯π¦^2 Ex 8.2, 3 Complete the table of products. For βπππ (β4π₯π¦)Γ3π₯^2 = β4Γπ₯Γπ¦Γ3Γπ₯^2 = (β4Γ3)Γ(π₯Γπ₯^2 )Γπ¦ = β12Γπ₯^3Γπ¦ = β12π₯^3 π¦ Ex 8.2, 3 Complete the table of products. For βπππ (β4π₯π¦)Γ(β4π₯π¦) = β4Γπ₯Γπ¦Γβ4Γπ₯Γπ¦ = (β4Γβ4)Γ(π₯Γπ₯)Γ(π¦Γπ¦) = 16Γπ₯^2Γπ¦^2 = 16π₯^2 π¦^2 Ex 8.2, 3 Complete the table of products. For βπππ (β4π₯π¦)Γ7π₯^2 π¦ = β4Γπ₯Γπ¦Γ7Γπ₯^2Γπ¦ = (β4Γ7)Γ(π₯Γπ₯^2 )Γ(π¦Γπ¦) = β28Γπ₯^3Γπ¦^2 = β28π₯^3 π¦^2 Ex 8.2, 3 Complete the table of products. For βπππ (β4π₯π¦)Γ(β9π₯^2 π¦^2 ) = β4Γπ₯Γπ¦Γβ9Γπ₯^2Γπ¦^2 = (β4Γβ9)Γ(π₯Γπ₯^2 )Γ(π¦Γπ¦^2 ) = 36Γπ₯^3Γπ¦^3 = 36π₯^3 π¦^3 Ex 8.2, 3 Complete the table of products. For ππ^π π (7π₯^2 π¦)Γ2π₯ = 7Γπ₯^2Γπ¦Γ2Γπ₯ = (7Γ2)Γ(π₯^2Γπ₯)Γπ¦ = 14Γπ₯^3Γπ¦ = 14π₯^3 π¦ Ex 8.2, 3 Complete the table of products. For ππ^π π (7π₯^2 π¦)Γ(β5π¦) = 7Γπ₯^2Γπ¦Γβ5Γπ¦ = (7Γβ5)Γπ₯^2Γ(π¦Γπ¦) = β35Γπ₯^2Γπ¦^2 = β35π₯^2 π¦^2 Ex 8.2, 3 Complete the table of products. For ππ^π π (7π₯^2 π¦)Γ3π₯^2 = 7Γπ₯^2Γπ¦Γ3Γπ₯^2 = (7Γ3)Γ(π₯^2Γπ₯^2 )Γπ¦ = 21Γπ₯^4Γπ¦ = 21π₯^4 π¦ Ex 8.2, 3 Complete the table of products. For ππ^π π (7π₯^2 π¦)Γ(β4π₯π¦) = 7Γπ₯^2Γπ¦Γβ4Γπ₯Γπ¦ = (7Γβ4)Γ(π₯^2Γπ₯)Γ(π¦Γπ¦) = β28Γπ₯^3Γπ¦^2 = β28π₯^3 π¦^2 Ex 8.2, 3 Complete the table of products. For ππ^π π (7π₯^2 π¦)Γ(7π₯^2 π¦) = 7Γπ₯^2Γπ¦Γ7Γπ₯^2Γπ¦ = (7Γ7)Γ(π₯^2Γπ₯^2 )Γ(π¦Γπ¦) = 49Γπ₯^4Γπ¦^2 = 49π₯^4 π¦^2 Ex 8.2, 3 Complete the table of products. For ππ^π π (7π₯^2 π¦)Γ(β9π₯^2 π¦^2 ) = 7Γπ₯^2Γπ¦Γβ9Γπ₯^2Γπ¦^2 = (7Γβ9)Γ(π₯^2Γπ₯^2 )Γ(π¦Γπ¦^2 ) = β63Γπ₯^4Γπ¦^3 = β63π₯^4 π¦^3 Ex 8.2, 3 Complete the table of products. For βππ^π π^π (β9π₯^2 π¦^2 )Γ2π₯ = β9Γπ₯^2Γπ¦^2Γ2Γπ₯ = (β9Γ2)Γ(π₯^2Γπ₯)Γπ¦^2 = β18Γπ₯^3Γπ¦^2 = β18π₯^3 π¦^2 Ex 8.2, 3 Complete the table of products. For βππ^π π^π (β9π₯^2 π¦^2 )Γβ5π¦ = β9Γπ₯^2Γπ¦^2Γβ5Γπ¦ = (β9Γβ5)Γπ₯^2Γ(π¦^2Γπ¦) = 45Γπ₯^2Γπ¦^3 = 45π₯^2 π¦^3 Ex 8.2, 3 Complete the table of products. For βππ^π π^π (β9π₯^2 π¦^2 )Γ(3π₯^2) = β9Γπ₯^2Γπ¦^2Γ3Γπ₯^2 = (β9Γ3)Γ(π₯^2Γπ₯^2 )Γπ¦^2 = β27Γπ₯^4Γπ¦^2 = β27π₯^4 π¦^2 Ex 8.2, 3 Complete the table of products. For βππ^π π^π (β9π₯^2 π¦^2 )Γ(β4π₯π¦) = β9Γπ₯^2Γπ¦^2Γβ4Γπ₯Γπ¦ = (β9Γβ4)Γ(π₯^2Γπ₯)Γ(π¦^2Γπ¦) = 36Γπ₯^3Γπ¦^3 = 36π₯^3 π¦^3 Ex 8.2, 3 Complete the table of products. For βππ^π π^π (β9π₯^2 π¦^2 )Γ7π₯^2 π¦ = β9Γπ₯^2Γπ¦^2Γ7Γπ₯^2Γπ¦ = (β9Γ7)Γ(π₯^2Γπ₯^2 )Γ(π¦^2Γπ¦) = β63Γπ₯^4Γπ¦^3 = β63π₯^4 π¦^3 Ex 8.2, 3 Complete the table of products. For βππ^π π^π (β9π₯^2 π¦^2 )Γ(β9π₯^2 π¦^2 ) = β9Γπ₯^2Γπ¦^2Γβ9Γπ₯^2Γπ¦^2 = (β9Γβ9)Γ(π₯^2Γπ₯^2 )Γ(π¦^2Γπ¦^2 ) = 81Γπ₯^4Γπ¦^4 = 81π₯^4 π¦^4 Note: π₯π Γπ₯π = π₯^(π + π) So, the completed table looks like