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    Add and subtract

            (ii) mn+5-2,mn+3

adding the following terms we will get Subtracting  We will get

    Add and subtract

            (i)  m-n,m+n

Adding   Will give the result as follows Subtracting  Will give the result as follows

  Classify the following expressions as a monomial, a binomial or a trinomial:

           a,a+b.ab+a+b,ab+a+b-5,xy,xy+5,5x^{2}-x+2,4pq-3q+5p,7,4m-7n+10,4mn+7.

Monomial: a, xy, 7 binomial: a+b, xy+5, 4mn+7 Trinomial: ab+a+b, 5x2-x+2, 4pq-3q+5p, 4m-7n+10 Polynomial with 4 terms: ab+a+b-5

Q.1.     Group the like terms together from the following:

            (i) 12x,  12 ,  -25x,  -25-25y1x12yy

The like terms are grouped below Group 1: , ,  Group 2: , ,  Group 3: , , 

    Identify the coefficients of the terms of following expressions:

             4x-3y,a+b+5,2y+5,2xy

 

i)  has two terms 4x and -3y the coefficient of x is 4 and the coefficient of y is -3 ii) a+b+5 has 3 terms a,b and a constant that is 5. the coefficient of a is 1 and b is also 1. Constant terms have no coefficient  iii) 2y+5 has two terms 2y and 5 which is constant.  The coefficient of y is 2. Constant terms have no coefficient  iv) 2xy has only one term which is 2xy and the coefficient of xy is 2

    Write three expressions each having 4 terms.

We can write as many expressions we need with 4 terms. Following are a few examples of expression with 4 terms

    What are the terms in the following expressions? Show how the terms are formed. Draw a tree diagram for each expression:

              8y+3x^{2},7mn-4,2x^{2}y.

  The terms in the expression are        is obtained by adding the product of 8 and y with the product of 3 x and x the tree diagram for the expression is given below  has two terms 7mn and 4 and the expression is obtained by subtracting 4 from the product of 7,m and n. The tree diagram is shown below.  has only one term, that is the expression itself. The expression is formed by multiplying...

 Describe how the following expressions are obtained:

         7xy+5, x^{2} y,4x^{2}-5x

  the above expression is obtained by adding 7xy with 5. Here 7xy is obtained by multiplying 7,x and y   the above expression is obtained by subtracting the product of 5 and x from the product of 4,x and x

Q. 2.     Use the given algebraic expression to complete the table of number patterns.

             

Below you can find the table of number patterns:

Q. 1.     Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

           

              

             

                        If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. How many segments are required to form 5, 10, 100 digits of the kind 

The number of segments required to form n of each digits shown above are 5n + 1, 3n + 1 and 5n + 2 When n = 5 When n = 10 When n = 100    

Q. 10.     Simplify the expression and find its value when a=5 and b=-3\; .2(a^{2}+ab)+3-ab

When a = 5 and b = -3 the value 2( a2 + ab ) + 3 - ab = 38

Q. 9.     What should be the value of a if the value of 2x^{2}+x-a equals to 5, when x=0?

Therefore for a = -5 when the value of x=0

Q. 8.    (ii) If p=-10, find the value of p^{2}-2p-100

If p = -10 the value of p2 - 2p - 100 = 20

Q. 8.     (i) If z=10,  find the value of z^{3}-3(z-10)

If z = 10 the value of z3 - 3( z - 10 ) = 1000

Q. 7.     Simplify these expressions and find their values if x=3,a=-1,b=-2.

            (i)  3x-5-x+9

            (ii)  2-8x+4x+4

            (iii)  3a+5-8a+1

            (iv) 10-3b-4-5b

            (v)  2a-2b-4-5+a

The expression is simplified as follows and also obtained their values (i) (ii) (iii) (iv) (v)

Q. 6.     Simplify the expressions and find the value if x is equal to 2 

             (iv)  4(2x-1)+3x+11

If x is equal to 2 the value of 4( 2x - 1 ) + 3x + 11 = 29

Q. 6.     Simplify the expressions and find the value if x is equal to 2

             (iii)  6x+5(x-2)

If x is equal to 2 the value of  6x + 5( x - 2 ) = 12

Q. 6.     Simplify the expressions and find the value if x is equal to 2

              (ii)  3(x+2)+5x-7

If x is equal to 2 the value of 3( x + 2 ) + 5x - 7 = 15

Q. 6.     Simplify the expressions and find the value if x is equal to 2

              (i)  x+7+4(x-5)

If x is equal to 2 the value of x + 7 + 4( x - 5 ) = -3

Q. 5.     When a=0,b=-1, find the value of the given expressions:

             (iv)  a^{2}+ab+2

When a = 0 and b = -1 the value of the given expression a2 + ab + 2 = 2
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