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Q. 6.    (b) From the sum of 4+3x and 5-4x+2x^{2},subtract the sum of 3x^{2}-5x and -x^{2}+2x+5.

On subtracting the sum of and  from the sum of   and  we get 

Q. 6.     (a) From the sum of 3x-y+11 and-y-11, subtract 3x-y-11.

On subtracting 3x - y - 11 from the sum of 3x - y + 11 and -y - 11 we get -y + 11

Q. 5.     What should be taken away from 3x^{2}-4y^{2}+5xy+20  to obtain -x^{2}-y^{2}+6xy+20 ?

Let the term be a which must be taken away from 3x2 - 4y2 + 5xy + 20 to obtain -x2 - y2 + 6xy + 20 4x2 - 3y2 - xy must be taken away from 3x2 - 4y2 + 5xy + 20 to obtain -x2 - y2 + 6xy + 20

Q. 4.    (b) What should be subtracted from 2a+8b+10  to get -3a+7b+16 ?

Let the term be c which must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16 5a + b - 6 must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16

Q. 4.     (a) What should be added to x^{2}+xy+y^{2} to obtain 2x^{2}+3xy?

Let the term be a which must be added to x2 + xy + y2 to obtain 2x2 + 3xy x2 + 2xy - y2 should be added to x2 + xy + y2 to obtain 2x2 + 3xy

Q. 3.     Subtract:

            (i)  -5y^{2} from y^{2}

            (ii) 6xy from -12xy

            (iii) (a-b) from (a+b)

            (iv)   a(b-5) from b(5-a)

            (v)  -m^{2}+5mn from 4m^{2}-3mn+8

            (vi)  -x^{2}+10x-5 from 5x-10

            (vii) 5a^{2}-7ab+5b^{2} from 3ab-2a^{2}-2b^{2}

            (viii) 4pq-5q^{2}-3p^{2} from 5p^{2}+3q^{2}-pq

The given terms are subtracted as follows (i) (ii) (iii) (iv) (v)   (vi) (vii) (viii)

Q. 2.     Add:

            (i)  3mn,-5mn,8mn,-4mn

            (ii)  t-8tz,3tz-z,z-t

            (iii) -7mn+5,12mn+2,9mn-8,-2mn-3

           (iv) a+b-3,b-a+3,a-b+3

           (v)  14x+10y-12xy-13,18-7x-10y+8xy,4xy

           vi)  5m-7n,3n-4m+2,2m-3mn-5

          (vii)  4x^{2}y,-3xy^{2},-5xy^{2},5x^{2}y

          (viii)  3p^{2}q^{2}-4pq+5,-10 p^{2}q^{2},15+9pq+7p^{2}q^{2}

          (ix)  ab-4a,4b-ab,4a-4b

          (x) x^{2}-y^{2}-1,y^{2}-1-x^{2},1-x^{2}-y^{2}

The given terms are added as follows

Q. 1.     Simplify combining like terms:

             (vi) (3y^{2}+5y-4)-(8y-y^{2}-4)

(3y2 + 5y - 4) - (8y - y2 - 4) = 3y2 + 5y - 4 - 8y + y2 + 4 = (3 + 1)y2 + (5 - 8)y - 4 + 4 = 4y2 - 3y  The simplified expression is 4y2 - 3y 

Q. 1.     Simplify combining like terms: 

             (v)   5x^{2}y-5x^{2}+3yx^{2}-3y^{2}+x^{2}-y^{2}+8xy^{2}-3y^{2}

5x2y - 5x2 + 3yx2 - 3y2 + x2 - y2 + 8xy2 - 3y2 = (5 + 3 )x2y + (-5 + 1)x2 + (-3 - 1 - 3)y2 + 8xy2 = 8x2y - 4x2 - 7y2 + 8xy2 The simplified expression is 8x2y - 4x2 - 7y2 + 8xy2

Q. 1.     Simplify combining like terms: 

             (iv)  3a-2b-ab-(a-b+ab)+3ab+b-a

3a - 2b - ab - (a - b + ab) + 3ab + b - a = 3a - 2b - ab - a + b - ab + 3ab + b - a = (3 - 1 - 1)a + (-2 + 1 +1)b + (-1 - 1 + 3)ab = a + ab The simplified expression is a + ab.

Q. 1.     Simplify combining like terms:

             (iii)  p-(p-q)-q-(q-p)

p - (p - q) - q - (q - p) = p - p + q - q - q + p = p - p + p + q - q -q = p - q The simplified expression is p - q.

Q. 1.     Simplify combining like terms:

             (ii)  -z^{2}+13z^{2}-5z+7z^{3}-15z

-z2 + 13z2 - 5z + 7z3 - 15z = (-1 + 13)z2 + (-5 - 15)z +7z3 =12z2 - 20z + 7z3 The simplified expression is 12z2 - 20z + 7z3

Q. 1.     Simplify combining like terms:

             (i) 21b-32+7b-20b

21b - 32 + 7b -20b = (21 + 7 - 20)b -32 = 8b - 32 The simplified expression is 8b - 32.
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