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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)

(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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