Algebraic Expressions and Identities

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Question
CBSEENMA8002855

Add: 9xy - 3yz + 2zx; 2xz + 9xy - 4y and -2xz + 5x + 3xy.

Solution

We write the expressions in separate rows, keeping like terms in the same column:

        9xy -3yz + 2zx
    +  9xy        + 2zx - 4y
     + 3xy         - 2 zx + 5x
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   21xy -3yz + 2zx -4y +5x
In the above example, -4y and 5x are carried over as they are, because they have no like terms. II. xz is same as zx.

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Question
CBSEENMA8002856

Subtract 6x2 – 5y2 + 7y – 4 from 82 – 5xy + 9y2 + 6x - 4y

Solution

We know that subtraction of a number is the same as addition of its additive inverse. We have
8x2 -5xy + 9y2+6x - 4y
6x2          - 5y2       + 7y - 4
(-)          (+)      (-)     (+)
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 2x2 -5xy + 14y2+6x -11y + 4

Question
CBSEENMA8002857

Give five examples of expressions containing one variable and five examples of expressions containing two variables.

Solution

(a) Five examples containing one variable are:

(i) x – 4 (ii) 5 – y (iii) 2x + 5

(iv) 10x + 4 (v) 11 – z

(b) Five examples containing two variables are:

(i) 7x – 2y (ii) 5x + 2y – 10 (iii) 6x + z – 2

(iv) 15y – z (v) 9x – 10z

Question
CBSEENMA8002859

Classify the coefficient of each term in the expression
x2y2 – 10x2y + 5xy2 – 20.

Solution

Coefficient of x2y2 is 1.

Coefficient of x2y is –10. Coefficient of xy2 is 5.