Question 15 Marks
Identify like terms in the following: $10 pq, 7 p, 8 q,-p^2q^2,-7 qp,-100 q,-23,12 q^2p^2,-5 p^2, 41,2405 p, 78 qp, 13 p^2qp^2, 701 p^2$
AnswerThe given terms and their factors are shown in the following table:
| Expression |
Variable Factors |
| $10pq$ |
$p, q$ |
| $7p$ |
$p$ |
| $8q$ |
$q$ |
| $– p^2q^2$ |
$p, p, q, q$ |
| $– 7qp$ |
$q, p$ |
| $– 100q$ |
$q$ |
| $– 23$ |
Constant |
| $12q^2p^2$ |
$q, q, p, p$ |
| $– 5p^2$ |
$p, p$ |
| $41$ |
Constant |
| $2405p$ |
$p$ |
| $78qp$ |
$q, p$ |
| $13p^2q$ |
$p, q, p$ |
| $qp^2$ |
$q, p, p$ |
| $701p^2$ |
$p, p$ |
So, From the above table we conclude that sets of like terms are
$i. 10pq, –7qp, 78qp :$ As both have common variable factors as $p$ and $q$
$ii. 7p, 2405p:$ As both have common variable factor as $p$
$iii. 8q, – 100q :$ As both have common variable factor as $q$
$iv. –p^2q^2, 12q^2p^2:$ As both have common variable factors as $p, q, q$ and $q$
$v. –23, 41 :$ As both terms are constant and don’t have any variable factor.
$vi. –5p^2, 701p^2:$ As both have common variable factors as $p$ and $p.$
$vii. 13p^2q, qp^2:$ As both have common variable factors as $p, p$ and $q.$ View full question & answer→Question 25 Marks
Identify like terms among the following: $-x y^2,-4 y x^2, 8 x^2, 2 x y^2, 7 y,-11 x^2,-100 x,-11 y x, 20 x^2 y,-6 x^2, y, 2 x y, 3 x$
AnswerHere, the given terms can be tabulated as:
| Expression |
Variable Factors |
| $– xy^2$ |
$x, y, y$ |
| $– 4yx^2$ |
$y, x, x$ |
| $8x^2$ |
$x, x$ |
| $2xy^2$ |
$x, y, y$ |
| $7y$ |
$y$ |
| $– 11x^2$ |
$x,x$ |
| $– 100x$ |
$x$ |
| $– 11yx$ |
$y, x$ |
| $20x^2y$ |
$x, x, y$ |
| $– 6x^2$ |
$x, x$ |
| $y$ |
$y$ |
| $2xy$ |
$x, y$ |
| $3x$ |
$x$ |
So, From the above table we conclude that sets of like terms are:
$i. -xy^2, 2xy^2:$ As both have common variable factors as $x, y$ and $y$
$ii. -4yx^2, 20x^2y:$ As both have common variable factors as $x, x$ and $y$
$iii. 8x^2 , -11x^2, -6x^2:$ As both have common variable factors as $x$ and $x$
$iv. -11yx, 2xy :$ As both have common variable factors as $x$ and $y$
$v. -100x, 3x :$ As both have common variable factor as $x$
$vi. 7y, y :$ As both have common variable factor as $y$ View full question & answer→Question 35 Marks
Identify terms and factors in the expressions given below:
$a. – 4x + 5$
$b. – 4x + 5y$
$c. 5y + 3y^2$
$d. xy + 2x^2 y^2$
$e. pq + q$
$f. 1.2 ab – 2.4 b + 3.6 a$
$g. \frac{3}{4} x+\frac{1}{4}$
$h. 0.1 p^2 + 0.2 q^2$
AnswerThe required information is provided below in the table:
| S.No |
Expression |
Terms |
Factors |
| $a$ |
$- 4x + 5$ |
$- 4x$
$5$ |
$-4, x$
$5$ |
| $b$ |
$- 4x + 5y$ |
$- 4x$
$5y$ |
$-4, x$
$5, y$ |
| $c$ |
$5y + 3y^2$ |
$5y$
$3y^2$ |
$5, y$
$3, y, y$ |
| $d$ |
$xy + 2x^2y^2$ |
$xy$
$2x^2y^2$ |
$x, y$
$2, x, x, y, y$ |
| $e$ |
$pq + q$ |
$p q$
$q$ |
$p, q$
$q$ |
| $f$ |
$1.2 a b - 2.4 b + 3.6 a$ |
$1.2 ab$
$-2.4 b$
$3.6 a$ |
$1.2, a, b$
$-2.4, b$
$3.6, a$ |
| $g$ |
$\frac{3}{4} x+\frac{1}{4}$ |
$\frac{3}{4} x$
$\frac{1}{4}$ |
$\frac{3}{4}, x$
$$$\frac{1}{4}$ |
| $h$ |
$0.1 \mathrm{p}^{2}+0.2 \mathrm{q}^{2}$ |
$0.1 \mathrm{p}^{2}$
$0.2 \mathrm{q}^{2}$ |
$0.1, p, p$
$0.2, q, q$ |
View full question & answer→Question 45 Marks
From the sum of $2 y^2+3 y z,-y^2-y z-z^2$ and $y z+2 z^2$, subtract the sum of $3 y^2-z^2$ and $-y^2+y z+z^2$.
AnswerWe first add $2 y^2+3 y z,-y^2-y z-z^2$ and $y z+2 z^2$, as follows:
$.....(i)$
We then add $3 y^2-z^2$ and $-y^2+y z+z^2$, as follows:
$.....(ii)$
Now, we subtract sum $(ii)$ from the sum $(i)$ and the result is shown below:
View full question & answer→Question 55 Marks
State with reasons, which of the following pairs of terms are like terms and which are unlike terms:
$i. 7x, 12y$
$ii. 15x, –21x$
$iii. – 4\ ab, 7\ ba$
$iv. 3\ xy, 3x$
$v. 6\ xy^2 , 9\ x^2 y$
$vi. pq^2 , – 4\ pq^2$
$vii. mn^2 , 10\ mn$
AnswerFollowing table represents all the required information:
| S. No. |
Pair |
Factors |
Algebraic
factors same
or different |
Like$/$Unlike terms |
Remarks |
| $(i)$ |
$7x$
$12y$ |
$\left.\begin{array}{l} {7, x} \\ {12, y} \end{array}\right\}$ |
Different |
Unlike |
The variables in the terms are different. |
| $(ii)$ |
$15x$
$–21x$ |
$\left.\begin{array}{l} {15, x} \\ {-21, x} \end{array}\right\}$ |
Same |
Like |
Terms have opposite sign and different numerical coefficients. |
| $(iii)$ |
$-4ab$
$7 ba$ |
$\left.\begin{array}{l} {-4, a, b} \\ {7, a, b} \end{array}\right\}$ |
Same |
Like |
Remember $ab = ba$ |
| $(iv)$ |
$3xy$
$3x$ |
$\left.\begin{array}{c} {3, x, y} \\ {3, x} \end{array}\right\}$ |
Different |
Unlike |
The variable $y$ is only in one term. |
| $(v)$ |
$6xy^2
9x^2y$ |
$\left.\begin{array}{l} {6, x, y, y} \\ {9, x, x, y} \end{array}\right\}$ |
Different |
Unlike |
The variables in the two terms match, but their powers do not match. |
| $(vi)$ |
$pq^2
4pq^2$ |
$\left.\begin{array}{c} {1, p, q, q} \\ {-4, p, q, q} \end{array}\right\}$ |
Same |
Like |
Note, numerical factor $1$ is not shown. |
View full question & answer→Question 65 Marks
What are the coefficients of y in the following expressions?
$4x – 3y, 8 + yz, yz^2 + 5, my + m$
AnswerFollowing table gives all the required information, regarding the terms containing $x$ and the coefficients of $x$ in those terms.
| S. No. |
Expression |
Term with factor y |
Coefficient of |
| $(i)$ |
$4x – 3y$ |
$– 3y$ |
$–3$ |
| $(ii)$ |
$8 + yz$ |
$yz$ |
$z$ |
| $(iii)$ |
$yz^2 + 5$ |
$yz^2$ |
$z^2$ |
| $(iv)$ |
$my + m$ |
$my$ |
$m$ |
View full question & answer→Question 75 Marks
What are the coefficients of x in the following expressions?
$4x – 3y, 8 – x + y, y^2 x – y, 2z – 5xz$
AnswerIn each of the following expressions we look for a term with $x$ as its one of the factors. The remaining part of that term is the coefficient of $x.$
| S. No |
Expression |
Term with Factor $x$ |
Coefficient of $x$ |
| $(i)$ |
$4x – 3y$ |
$4x$ |
$4$ |
| $(ii)$ |
$8 – x + y$ |
$–x$ |
$–1$ |
| $(iii)$ |
$y^2 x – y$ |
$y^2 x$ |
$y^2$ |
| $(iv)$ |
$2z – 5xz$ |
$– 5xz$ |
$– 5z$ |
View full question & answer→Question 85 Marks
Identify, in the expressions, the terms which are not constants. Give their numerical coefficients:
$xy + 4, 13 – y^2 , 13 – y + 5y^2 , 4p^2 q – 3pq^2 + 5$
AnswerFollowing table gives all the required solution:
| S. No. |
Expression |
Term (which is not a Constant) |
Numerical Coefficient |
| $(i)$ |
$xy + 4$ |
$xy$ |
$1$ |
| $(ii)$ |
$13 – y^2$ |
$– y^2$ |
$–1$ |
| $(iii)$ |
$13 – y + 5y^2$ |
$–y
5y^2$ |
$–1$
$5$ |
| $(iv)$ |
$4p^2 q – 3pq^2 + 5$ |
$4p^2 q
– 3pq$ |
$4$
$-3$ |
View full question & answer→