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Q. 6.    (b) From the sum of  and subtract the sum of and .

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

Q. 6.     (a) From the sum of  and, subtract

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   to obtain

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   to get

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 to obtain

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)   from

(ii)  from

(iii)  from

(iv)    from

(v)   from

(vi)   from

(vii)  from

(viii)  from

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

(i)

(ii)

(iii)

(iv)

(v)

vi)

(vii)

(viii)

(ix)

(x)

The given terms are added as follows

Q. 1.     Simplify combining like terms:

(vi)

(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)

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

Q. 1.     Simplify combining like terms:

(ii)

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