To do: To 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^2y, \ -3xy^2, \ -5xy^2, \ 5x^2y$$(viii)$. $3p^2q^2-4pq+5, \ -10p^2q^2, \ 15+9pq+7p^2q^2$$(ix)$. ... Read More

To do: To 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$$(viii)$. $4pq-5q^2-3p^2$ from $5p^2+3q^2-pq$Solution:i) $-5y^2$ from $4y^2$$=y^{2\ }-(-5y^2)$$=y^2+5y^{2\ }=\ 6y^2$ii) $6xy$ from $-12xy$$=-12xy-(6xy)$$=-18xy$iii) $(a-b)$ from $(a+b)$$=(a+b)-(a-b)$$=2b$iv) $a(b-5)$ from $b(5-a)$$=b(5-a)-a(b-5)$$=5b-ab-ab+5a$$=5a+5b-2ab$v) $-m^2+5mn$ from $4m^2-3mn+8$$=(4m^2-3mn+8)-(-m^2+5mn)$$=4m^2+m^2-3mn-5m+8$$=5m^2-8mn+8$vi) $-x^2+10x-5$ from $5x-10$$=(5x-10)-(-x^2+10x-5)$$=x^{2}+5x-10x-10+5$$=x^{2}-5x-5$vii) $5a^2-7ab+5b^{2}$ ... Read More

Given: $(a)$ Terms $x^2+xy+y^2$ and $2x^2+3xy$.$(b)$. Terms $2a+8b+10$ and $-3a+7b+16$To do: $(a)$ This is to find out what should be added to $x^2+xy+y^2$ to obtain $2x^2+3xy$.$(b)$ This is to find out what should be subtracted from $2a+8b+10$ to get $-3a+7b+16$Solution: $(a)$. Let's assume $'a'$ to be the required term$=a+(x^2+y^2+xy)=2x^2+3xy$$a=2x^2+3xy-(x^2+y^2+xy)$$a=2x^2+3xy-x^2-y^2-xy$$a=x^2-y^2+2xy $Therefore, $x^2-y^2+2xy$ should be ... Read More

Given: Terms $3x^2-4y^2+5xy+20$ and $– x^2-y^2+6xy+20$. To do: This is to find out what should be taken from $3x^2-4y^2+5xy+20$ to get $- x^2-y^2+6xy+20$.Solution: Let us assume $a$ be the required termThen, $3x^2-4y^2+5xy+20-a=-x^2-y^2+6xy+20$$a=3x^2-4y^2+5xy+20-(-x^2-y^2+6xy+20)$$a=3x^2-4y^2+5xy+20+x^2+y^2-6xy-20$$a=3x^2+x^2-4y^2+y^2+5xy-6xy+20-20$$a=4x^2-3y^2-xy$Therefore, $4x^2-3y^2-xy$ should be taken from $3x^2-4y^2+5xy+20$ to get $- x^2-y^2+6xy+20$.Read More

Given: $(i)$. $m-2$$(ii)$. $3m-5$$(iii)$. $9-5m$$(iv)$. $3m^2-2m-7$$(v)$. $\frac{5m}{2}-4$To do: To find the value of given expressions if $m=2$.Solution: $(i)$. $m-2$Putting $m=2$$=2-2$$=0$$(ii)$. $3m-5$Putting $m=2$$=3(2)-5$$=6-5$$=1$$(iii)$. $9-5m$Putting $m=2$$=9-5(2)$$=9-10$$=-1$$(iv)$. $3m^2-2m-7$Putting $m=2$$=3(2)^2-2(2)-7$$=12-4-7$$=1$$(v)$. $\frac{5m}{2}-4$Putting $m=2$$=\frac{5(2)}{2}-4$$=5-4$$=1$Read More

Given: $(i)$. $4p+7$$(ii)$. $-3p^2+4p+7$$iii)$. $-2p^3-3p^2+4p+7$ To do: To find the value of if $p=-2$. Solution: $(i)$. $4p+7$ Putting $p=-2$ $=4(-2)+7$ $=-8+7$ $=-1$ $(ii)$. $-3p^2+4p+7$ Putting $p=-2$ $=-3(-2)^2+4(-2)+7$ $=-3(4)-8+7$ $=-12-8+7$ $=-13$ $(iii)$. $-2p^3-3p^2+4p+7$ Putting $p=-2$ $=-2(-2)^3-3(-2)^2+4(-2)+7$ $=-2(-8)-3(4)-8+7$ $=16-12-8+7$ $=3$Read More

Given: $(i)$. $2x-7$$(ii)$. $-x+2$$(iii)$. $x^2+2x+ 1$$(iv)$. $2x^2-x-2$ To do: To find the value of the given expressions, when $x=-1$Solution: $(i)$. $2x-1$$=2\times\ (-1)-7$$=-9$$(ii)$. $-x+2$$=-(-1)+2$$=1+2$$=3$$(iii)$. $x^2+2x+1$$=(-1)\ \times\ (-1)+2\ \times\ (-1)+1$$=1-2+1$$=0$$(iv)$. $2x^2-x-2$$=2(-1)\ \times\ (-1)-(-1)-2$$=2+1-2=1$Read More

Given:$(i)$. $a^2+b^2$$(ii)$. $a^2+ab+b^2$$(iii)$. $a^{2}-b^2$To do: To find the value of the given expression if $a=2$ and $b=-2$.Solution:$(i)$. $a^2+b^2$Putting $a=2$ and $b=-2$$=2^2+(-2)^2$$=4+4$$=8$$(ii)$. $a^2+ab+b^2$Putting $a=2$ and $b=-2$$=2^2+2(-2)+(-2)^2$$=4-4+4$$=4$$(iii)$. $a^{2}-b^2$ Putting $a=2$ and $b=-2$$=(2)^2-(-2)^2$$=4-4$$=0$Read More

Given: $(i)$. $2a+2b$$(ii)$. $2a^2+b^2+1$$(iii)$. $2a^2b+2ab^2+ab$$(iv)$. $a^2+ab+2$To do: To find the value of the given expressions when $a=0$, $b=-1$.Solution:$(i)$. $2a+2b$Putting $a=0$ and $b=-1$$=2(0)+2(-1)$$=0-2$$=-2$$(ii)$. $2a^2+b^2+1$Putting $a=0$ and $b=-1$$=2(0)^2+(-1)^2+1$$=0+1+1$$=2$$(iii)$. $2a^2b+2ab^2+ab$Putting $a=0$ and $b=-1$$=2(0)^2(-1)+2(0)(-1)^2+0(-1)$$=0+0+0$$=0$$(iv)$. $a^2+ab+2$Putting $a=0$ and $b=-1$$=0^2+(0)(-1)+2$$=0+0+2$$=2$Read More

Given: $(i)$. $x+7+4(x-5)$$(ii)$. $3(x+2)+5x-7$$(iii)$. $6x+5(x-2)$$(iv)$. $4(2x-1)+3x+11$To do: To simplify the expressions and find the value of $x$ is equal to $2$.Solution:$(i)$. $x+7+4(x-5)$$=x+7+4x-20$$=x+4x+7-20$$=5x+7-20$$=5x-13$$=5(2)-13$                                   If, $x=2$$=10-13$$=-3$$(ii)$. $3(x+2)+5x-7$$=3x+6+5x-7$$=8x-1$$=8(2) - 1$                  ... Read More