Addition and Subtraction of Algebraic Expressions

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  • Q1

    What should be added to x2 + xy to obtain 5x2 - xy?

    Marks:2
    Answer:

    (5x2 - xy ) - (x2 + xy )
    = 5x2 - xy - x2 - xy
    = 4x2 - 2xy
    Therefore , (4x2 - 2xy) should be added to x2 + xy to obtain 5x2 - xy.

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  • Q2

    Add 4x2 + 2xy – 4 and 7x2 – 3xy + 4.

    Marks:1
    Answer:

    4x2 + 2xy – 4 + 7x2 – 3xy + 4

    = x2(4 + 7) + xy(2 – 3) + 4 - 4

    = 11x2 – xy

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  • Q3

    Marks:5
    Answer:

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  • Q4

    By how much is 5x2y+ 4x4y2 greater than x4 – 4y2 + 4x2y?

    Marks:2
    Answer:

    To get the required expression, we will subtract
    x4 – 4y2 + 4x2y from 5x2y + 4x4y2.

    (5x2y + 4x4y2) – (x4 – 4y2 + 4x2y)

    = 5x2y + 4x4y2 x4 + 4y2 4x2y

    = 5x2y 4x2y + 4x4 x4y2 + 4y2

    = x2y + 3x4 + 3y2

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  • Q5

    Find the sum of 5xy2 + 2x2y, 2xy2– 7x2y + 2xy and x2y –5xy.

    Marks:2
    Answer:

    (5xy2 + 2x2y) + (2xy2 – 7x2y + 2xy) + (x2y –5xy)

    = 5xy2 + 2xy2 + 2x2y – 7x2y + x2y + 2xy – 5xy

    = 7xy2 – 4x2y – 3xy

    Hence, the sum is (7xy2 – 4x2y – 3xy).

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