Question 12 Marks
Add the following: $2 x^2 y,-4 x^2 y, 6 x^2 y,-5 x^2 y$
AnswerAdding the given terms,
We have,
$2 x^2 y+\left(-4 x^2 y\right)+\left(6 x^2 y\right)+\left(-5 x^2 y\right)$
$=2 x^2 y-4 x^2 y+6 x^2 y-5 x^2 y$
$=(2-4+6-5) x^2 y$
$=(8-9) x^2 y$
$=-x^2 y$
View full question & answer→Question 22 Marks
Add the following expressions:
$5 x^3+7+6 x-5 x^2, 2 x^2-8-9 x, 4 x-2 x^2+3 x^3, 3 x^3-9 x-x^2$ and $x-x^2-x^3-4$
AnswerRequired expression:
$=\left(5 x^3+7+6 x-5 x^2\right)+\left(2 x^2-8-9 x\right)+\left(4 x-2 x^2+3 x^3\right)+\left(3 x^3-9 x-x^2\right)+\left(x-x^2-x^3-4\right)$
Collecting positive and negative like terms together, we get
$5 x^3+3 x^3+3 x^3-x^3-5 x^2+2 x^2-2 x^2-x^2-x^2+6 x-9 x+4 x-9 x+x+7-8-4$
$=10 x^3-7 x^2-7 x-5$
View full question & answer→Question 32 Marks
Evaluate the following expressions for $x = -2, y = -1, z = 3$: $\text{x}^2+\text{y}^2+\text{z}^2-\text{xy}-\text{yz}-\text{zx}$
Answer$(-2)^2+\text{y}^2+\text{z}^2-\text{xy}-\text{yz}-\text{zx}$
$=(-2)^2+(-1)^2+(3)^2-(-2)(-1)-(-1)(3)-(3)(-2)$
$=4+1+9-2+3+6$
$=(4+1+9+3+6)-2$
$=23-2$
$=21$
View full question & answer→Question 42 Marks
Add the following expressions:
$x^3-2 x^2 y+3 x y^2-y^3, 2 x^3-5 x y^2+3 x^2 y-4 y^3$
AnswerAdding the given expressions,
We have,
$x^3-2 x^2 y+3 x y^2-y^3, 2 x^3-5 x y^2+3 x^2 y-4 y^3$
Collecting positive and negative like terms together, we get
$x^3+2 x^3-2 x^2 y+3 x^2 y+3 x y^2-5 x y^2-y^3-4 y^3$
$=3 x^3+x^2 y-2 x y^2-5 y^3$
View full question & answer→Question 52 Marks
Add the following: $7abc, -5abc, 9abc, -8abc$
AnswerAdding the given terms,
We have, $7abc + (-5abc) + (9abc) + (-8abc) $
$= 7abc - 5abc + 9abc - 8abc$
$ = (7 - 5 + 9 - 8)abc$
$ = (16 - 13)abc$
$ = 3abc$
View full question & answer→Question 62 Marks
Simplify the following algebraic expressions by removing grouping symbols: $2x + (5x - 3y)$
AnswerWe have, $2x + (5x - 3y)$ Since the $'+'$ sign precedes the parentheses,
we have to retain the sign of each term in the parentheses when we remove them.
$= 2x + 5x - 3y = 7x - 3y$
View full question & answer→Question 72 Marks
Add $2 x^2-3 x+1$ to the sum of $3 x^2-2 x$ and $3 x+7$.
AnswerSum of $3 x^2-2 x$ and $3 x+7$
$=\left(3 x^2-2 x\right)+(3 x+7)$
$=3 x^2-2 x+3 x+7$
$=\left(3 x^2+x+7\right)$
Now, required expression:
$=2 x^2-3 x+1+\left(3 x^2+x+7\right)$
$=2 x^2+3 x^2-3 x+x+1+7$
$=5 x^2-2 x+8$
View full question & answer→Question 82 Marks
Add the following expressions:
$a^4-2 a^3 b+3 a b^3+4 a^2 b^2+3 b^4,-2 a^4-5 a b^3+7 a^3 b-6 a^2 b^2+b^4$
AnswerAdding the given expressions,
We have,
$a^4-2 a^3 b+3 a b^3+4 a^2 b^2+3 b^4,-2 a^4-5 a b^3+7 a^3 b-6 a^2 b^2+b^4$
$a^4-2 a^3 b+3 a b^3+4 a^2 b^2+3 b^4-2 a^4-5 a b^3+7 a^3 b-6 a^2 b^2+b^4$
Collecting positive and negative like terms together, we get
$a^4-2 a^4-2 a^3 b+7 a^3 b+3 a b^3-5 a b^3+4 a^2 b^2-6 a^2 b^2+3 b^4+b^4$
$=-a^4+5 a^3 b-2 a b^3-2 a^2 b^2+4 b^4$
View full question & answer→Question 92 Marks
Simplify the following algebraic expressions by removing grouping symbols: $3x - (y - 2x)$
AnswerWe have, $3x - (y - 2x)$ Since the $'-'$ sign precedes the parentheses,
we have to change the sign of each term in the parentheses when we remove them.
Therefore, we have $3x - y + 2x = 5x - y$
View full question & answer→Question 102 Marks
Add the following expressions: $8a - 6ab + 5b, -6a - ab - 8b$ and $-4a + 2ab + 3b$
AnswerRequired expression: $= (8a - 6ab + 5b) + (-6a - ab - 8b) + (-4a + 2ab + 3b)$
Collecting positive and negative like terms together,
we get $8a - 6a - 4a - 6ab - ab + 2ab + 5b - 8b + 3b $
$= 8a - 10a - 7ab + 2ab + 8b - 8b$
$ = -2a - 5ab$
View full question & answer→Question 112 Marks
Identify the terms and also mention the numerical coefficients of those terms: $\text{7a}^2\text{bc},-\text{3ca}^2\text{b},-\frac52\text{abc}^2,\frac32\text{abc}^2,-\frac43\text{cba}^2$
Answer
| Like terms |
Numerical coefficients |
| $\Big\{7\text{a}^2\text{bc},-\text{3ca}^2\text{b},-\frac43\text{cba}^2\Big\}\Big\{-\frac52\text{abc}^2,\frac{3}{2}\text{abc}^2\Big\}$ |
$\Big\{7,-3,-\frac43\Big\}\Big\{-\frac52,\frac32\Big\}$ |
View full question & answer→Question 122 Marks
Add the following:
$x - 3y - 2z$
$5x + 7y - 8z$
$3x - 2y + 5z$
AnswerRequired expression: $= (x - 3y - 2z) + (5x + 7y - 8z) + (3x - 2y + 5z)$
Collecting positive and negative like terms together,
we get $x + 5x + 3x - 3y + 7y - 2y - 2z - 8z + 5z $
$= 9x - 5y + 7y - 10z + 5z $
$= 9x + 2y - 5z$
View full question & answer→Question 132 Marks
Simplify the following algebraic expressions by removing grouping symbols: $5a - (3b - 2a + 4c)$
AnswerWe have, $5a - (3b - 2a + 4c)$
Since the $'-'$ sign precedes the parentheses,
we have to change the sign of each term in the parentheses when we remove them.
= $5a - 3b + 2a - 4c = 7a - 3b - 4c$
View full question & answer→Question 142 Marks
Add the following:
$4ab - 5bc + 7ca$
$-3ab + 2bc - 3ca$
$5ab - 3bc + 4ca$
AnswerRequired expression: $= (4ab - 5bc + 7ca) + (-3ab + 2bc - 3ca) + (5ab - 3bc + 4ca)$
Collecting positive and negative like terms together,
we get $4ab - 3ab + 5ab - 5bc + 2bc - 3bc + 7ca - 3ca + 4ca $
$= 9ab - 3ab - 8bc + 2bc + 11ca - 3ca $
$= 6ab - 6bc + 8ca$
View full question & answer→Question 152 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$a-[2 b-\{3 a-(2 b-3 c)\}]$
View full question & answer→Question 162 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$a-[b-\{a-(b-1)+3 a\}]$
View full question & answer→Question 172 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$5 a-\{3 a-(2-a)+4\}$
View full question & answer→Question 182 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$3 x+2 y-\{x-(2 y-3)\}$
View full question & answer→Question 192 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$-2\left(x^2-y^2+x y\right)-3\left(x^2+y^2-x y\right)$
View full question & answer→Question 202 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$5 a-(3 b-2 a+4 c)$
View full question & answer→Question 212 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$3 x-(y-2 x)$
View full question & answer→Question 222 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$2 x+(5 x-3 y)$
View full question & answer→Question 232 Marks
Write each of the following statements by using appropriate grouping symbols: The subtraction of $x^2-y^2+4 x y$ from $2 x^2+y^2-3 x y$ is added to $9 x^2-3 y^2-x y$.
Answer$\left\{\left(2 x^2+y^2-3 x y\right)-\left(x^2-y^2+4 x y\right)\right\}+\left(9 x^2-3 y^2-x y\right)$
View full question & answer→Question 242 Marks
Write each of the following statements by using appropriate grouping symbols: Three times the sum of $2 x+y-\{5-(x-3 y)\}$ and $7 x-4 y+3$ is subtracted from $3 x-4 y+7$.
Answer$(3 x-4 y+7)-3[(2 x+y)-\{5-(x-3 y)\}+(7 x-4 y+3)]$
View full question & answer→Question 252 Marks
Write each of the following statements by using appropriate grouping symbols: The sum of $a-b$ and $3 a-2 b+5$ is subtracted from $4 a+2 b-7$.
Answer$(4 a+2 b-7)-\{(a-b)+(3 a-2 b+5)\}$
View full question & answer→Question 262 Marks
From: $x^3-5 x^2+3 x+1$, take away $6 x^2-4 x^3+5+3 x$
View full question & answer→Question 272 Marks
From: $1-5 y^2$, take away $y^3+7 y^2+y+1$
View full question & answer→Question 282 Marks
Subtract: $x^3+2 x^2 y+6 x y^2-y^3$ from $y^3-3 x y^2-4 x^2 y$
Answer$2 y^3-9 x y^2-6 x^2 y-x^3$
View full question & answer→Question 292 Marks
From: $7+x-x^2$, take away $9+x+3 x^3+7 x^3$
View full question & answer→Question 302 Marks
Subtract: $-x^2-3 z$ from $5 x^2-y+z+7$
View full question & answer→Question 312 Marks
Add the following: $2 x^2 y,-4 x^2 y, 6 x^2 y,-5 x^2 y$
View full question & answer→Question 322 Marks
Add the following: $-5 x y$ and $9 x y$
View full question & answer→Question 332 Marks
From: $p^3-4+3 p^2$, take away $5 p^2-3 p^3+p-6$
View full question & answer→Question 342 Marks
Subtract: $6 x^3-7 x^2+5 x-3$ from $4-5 x+6 x^2-8 x^3$
Answer$-14 x^3+13 x^2-10 x+7$
View full question & answer→Question 352 Marks
Add the following: $7 a b c,-5 a b c, 9 a b c,-8 a b c$
View full question & answer→Question 362 Marks
Add the following: $3 x$ and $7 x$
View full question & answer→Question 372 Marks
How much does $a^2-3 a b+2 b^2$ exceed $2 a^2-7 a b+9 b^2 ?$
View full question & answer→Question 382 Marks
How much is $x^2-2 x y+3 y^2$ less than $2 x^2-3 y^2+x y$ ?
View full question & answer→Question 392 Marks
How much is $x-2 y+3 z$ greater than $3 x+5 y-7$ ?
View full question & answer→Question 402 Marks
Write the coefficient of $x^2$ in the following:
$-\frac{3}{2} a x^2+y x$
View full question & answer→Question 412 Marks
Write the coefficient of $x^2$ in the following:
$\frac{5}{7} x^2 z$
View full question & answer→Question 422 Marks
Write the coefficient of $x^2$ in the following:
$5 x^2 y z$
View full question & answer→Question 432 Marks
Write the coefficient of $x^2$ in the following:
$-3 x^2$
View full question & answer→Question 442 Marks
Write the coefficient of $x$ in the following:
$-7 a x$
View full question & answer→Question 452 Marks
Write the coefficient of $x$ in the following:
$x y z$
View full question & answer→Question 462 Marks
Write the coefficient of $x$ in the following:
$-7 x y$
View full question & answer→Question 472 Marks
Write the coefficient of $x$ in the following:
$-12 x$
View full question & answer→Question 482 Marks
Identify the like terms in the following algebraic expressions:
$a b c+a b^2 c+2 a c b^2+3 c^2 a b+b^2 a c-2 a^2 b c+3 c a b^2$
Answer$a b^2 c, 2 a c b^2, b^2 a c, 3 c a b^2$
View full question & answer→Question 492 Marks
Identify the like terms in the following algebraic expressions:
$3 x+4 x y-2 y z+\frac{5}{2} z y$
Answer$-2 y z, \frac{5}{2} z y$
View full question & answer→Question 502 Marks
Identify the like terms in the following algebraic expressions:
$a^2+b^2-2 a^2+c^2+4 a$
View full question & answer→Question 512 Marks
Evaluate each of the following expressions for $x=-2, y=-1, z=3$ :
$x^2+y^2+z^2-x y-y z-z x$
View full question & answer→Question 522 Marks
Evaluate each of the following expressions for $x=-2, y=-1, z=3$ :
$\frac{x}{y}+\frac{y}{z}+\frac{z}{x}$
View full question & answer→Question 532 Marks
Write the numerical coefficient of the following:
$-2 x^3 y^2 z$
View full question & answer→Question 542 Marks
Write the numerical coefficient of the following:
7abc
Question 552 Marks
Write the numerical coefficient of the following:
-6yz
Question 562 Marks
Write the numerical coefficient of the following:
xy