Given: $(i)$. $3x-5-x+9$$(ii)$. $2-8x+4x+4$$(iii)$. $3a+5-8a+1$$(iv)$. $10-3b-4-5b$$(v)$. $2a-2b-4-5+a$ To do: To simplify these expressions and find their values if $x=3, \ a=-1, \ b=-2$. Solution: $(i)$ $3x-5-x+9$ $=2x+4$ if $x=3$ $=2(3)+4$ $=6+4$ $=10$ $(ii)$. $2-8x+4x+4$ $=-8x+4x+4+2$ $=-4x+6−4x+6$ $=-4(3)+6$                            ... Read More

To do: $(i)$ To find the value of $z^3-3(z-10)$ if $z=10$. $(ii)$ To find the value of $p^2-2p-100$ if $p=-10$. Solution: $(i)$. $z^3-3(z-10)$ $=z^3-3z-30$ if $z=10$ $=10^3-3(10)+30$ $=1000 - 30+30$ $=1000$ $(ii)$. $p^2-2p-100$ If $p=-10$ $=(-10)^2-2(-10)-100$ $=100+20-100$ $=20$

Given: Expression: $2x^2+x-a$To do: To find the value of $a$ if the value of $2x^2+x-a$ equals to $5$, when $x=0$.Solution: From the question, it is given that $x=0$We have, $2\times 2+x-a=5$$a=2\times 2+x-5$Then, Substitute the value of $x$ in the Equation$a=(2\times 02)+0-5$$a=0+0-5$$a=-5$Read More

Given: Expression: $2(a^2+ab)+3-ab$To do: To simplify the Expression and Find its Value when $a=5$ and $b=-3$.Solution:From the question it is given that $a=5$ and $b=-3$We have, $=2a^2+2ab+3-ab$$=2a^2+ab+3$Then, Substitute the value of $a$ and $b$ in the Equation$=(2\times 5^2)+(5\times (-3))+3$$=(2\times 25)+(-15)+3$$=50 - 15+3$$=53-15$$=38$Read More

To do:We have to draw any line segment $\overline{PQ}$ and without measuring $\overline{PQ}$, we have to construct a copy of $\overline{PQ}$.Solution:Steps of construction:(i) First let us draw any line segment $\overline{PQ}$.(ii) Then by pointing the pointer of compasses on point P let us adjust the compasses to point Q.(iii) Let ... Read More

Given: $(a)$.$-xy^2, -4yx^2, \ 8x^2, \ 2xy^2, \ 7y, -11x^2, -100x, -11yx, \ 20x^{2}y, -6x^2, \ y, \ 2xy, \ 3x$$(b)$. $10pq, \ 7p, \ 8q, -p^2q^2, -7qp, -100q, -23, \ 12q^2p^2, -5p^2, \ 41, \ 2405p, \ 78qp, \ 13p^2q, \ qp^2, \ 701p^2$To do: To identify like terms in the ... Read More

To do: To get the algebraic expressions in the given cases using variables, constants, and arithmetic operations.Solution:$(i)$: Subtraction of $z$ from $y$.$y-z$$(ii)$: One-half of the sum of numbers $x$ and $y$.$\frac{1}{2}(x+y)$ or $\frac{x+y}{2}$$(iii)$: The number $z$ multiplied by itself.$z\times z=z^2$$(iv)$: One-fourth of the product of numbers $p$ and $q$.$\frac{1}{4}pq$ or $\frac{pq}{4}$$(v)$: Numbers $x$ and ... Read More

Given: $(i)$.  $(a)$. $x-3$         $(b)$. $1+x+x^2$             $(c)$. $y-y^3$$(d)$. $5xy^2+7x^2y$          $(e)$. $– ab +2b^2-3a^2$$(ii)$.   $(a)$. $-4x+5$           $(b)$. $-4x+5y$          $(c)$. $5y +3y^2$$(d)$. $xy+2x^2y^2$            $(e)$. $pq+q$       $(f)$. ... Read More

Given:Given $\overline{AB}$ of length $7.3\ cm$ and $\overline{CD}$ of length $3.4\ cm$.To do:We have to construct a line segment $\overline{XY}$ whose length is equal to the difference between the lengths of $\overline{AB}$ and $\overline{CD}$ and verify it by measurement.Solution: Steps of construction: (i) First let us take compasses and by ... Read More

Given:$\overline{AB}$ of length $3.9\ cm$.To do:We have to construct $\overline{PQ}$ that is twice that of $\overline{AB}$ and verify by measurement.Solution: Steps of construction: (i) First, let us draw a line 'l' and mark a point P on the line 'l'.(ii) Now, by taking the length of $\overline{AB}$ with compasses ... Read More