Question 11 Mark
Write all the terms of the following algebraic expressions:
3x
AnswerThe terms of the given algebraic expressions are as follows:
3x is the only term of the given algebraic expression.
View full question & answer→Question 21 Mark
Evaluate the following algebraic expressions for $x =1, y =-1, z =2, a =-2, b=1, c =-2$ :
$a x^2+b y^2-c z$
AnswerWe have $x =1, y =-1, z =2, a =-2, b=1$ and $c =-2$.
Thus,
$a x^2+b y^2-c z^2$
$=(-2)(1)^2+(1)(-1)^2-(-2)(2)^2$
$=-2 \times 1+1-(-2 \times 4)$
$=-2+1-(-8)$
$=-2+1+8$
$=-2+9$
$=7$
View full question & answer→Question 31 Mark
Write the coefficient of:
$x^3$ in $x^3+1$
AnswerThe coefficients are as follows:
The coefficient of $x^3$ is 1.
View full question & answer→Question 41 Mark
Place the last two terms of the following expressions in parentheses preceded by a minus sign:
3x - 2y - 5z - 4
AnswerWe have,
3x - 2y - 5z - 4
= 3x - 2y - (5z + 4)
View full question & answer→Question 51 Mark
Write all the terms of the following algebraic expressions:
$2 x^2-7$
AnswerThe terms of the given algebraic expressions are as follows:
$2 x^2$ and -7 are the terms of the given algebraic expression.
View full question & answer→Question 61 Mark
Place the last two terms of the following expressions in parentheses preceded by a minus sign:
$a^2+b^2-c^2+a b-3 a c$
AnswerWe have,
$a^2+b^2-c^2+a b-3 a c$
$=a^2+b^2-c^2-(-a b+3 a c)$
View full question & answer→Question 71 Mark
Write the coefficient of x in the following:-7ax
AnswerThe coefficients of x are as follows:
The numerical coefficient of x is -7a.
View full question & answer→Question 81 Mark
Write the coefficient of:
y in -3y
AnswerThe coefficients are as follows:
The coefficient of y is -3.
View full question & answer→Question 91 Mark
Write the constant term of the following algebraic expressions:
$x^2 y-x y^2+7 x y-3$
AnswerThe constant term of the given algebraic expressions is as follows:
The constant term in the given algebraic expressions is -3 .
View full question & answer→Question 101 Mark
Write the numerical coefficient of the following:
-6yz
AnswerThe numerical coefficient of the given terms is as follows:
The numerical coefficient in the term -6yz is -6.
View full question & answer→Question 111 Mark
Subtract:
$7 a^2 b$ from $3 a^2 b$
AnswerRequired expression:
$=3 a^2 b-7 a^2 b$
$=(3-7) a^2 b$
$=-4 a^2 b$
View full question & answer→Question 121 Mark
Simplify the following:
$12 a^2 b+3 b a^2$
AnswerSimplifying the given expressions,
We have,
$12 a^2 b+3 b a^2$
$=(12+3) a^2 b$
$=15 a^2 b$
View full question & answer→Question 131 Mark
Write the coefficient of 2 in the following:
$\frac57\text{x}^2\text{z}$
AnswerThe coefficient of $x^2$ is as follows:
The numerical coefficient of $x^2$ is $\frac57\text{z}.$
View full question & answer→Question 141 Mark
Write the numerical coefficient term in the following algebraic expressions:
$-\frac{5}{3}\text{x}^2\text{y}+\frac74\text{xyz}+3$
AnswerThe numerical coefficient term in the given algebraic expression is as follows.
| Term |
Coefficient |
| $-\frac53\text{x}^2\text{y}$ |
$-\frac53$ |
| $\frac74\text{xyz}$ |
$\frac74$ |
| $3$ |
$3$ |
View full question & answer→Question 151 Mark
Write the coefficient of x in the following:-12x
AnswerThe coefficients of x are as follows:
The numerical coefficient of x is -12.
View full question & answer→Question 161 Mark
Write the following statements by using appropriate grouping symbols:
Three times the sum of 2x + y - [5 - (x - 3y)] and 7x - 4y + 3 is subtracted from 3x - 4y + 7
AnswerThree times the sum of 2x + y - {5 - (x - 3y)} and 7x - 4y + 3
= 3[(2x + y - {5 - (x - 3y)}) + (7x - 4y + 3)]
This is subtracted from 3x - 4y + 7
Thus, the required expression is (3x - 4y + 7) - 3[(2x + y - {5 - (x - 3y)}) + (7x - 4y + 3)]
View full question & answer→Question 171 Mark
Write the coefficient of 2 in the following:
$-3 x^2$
AnswerThe coefficient of $x^2$ is as follows:
The numerical coefficient of $x^2$ is -3 .
View full question & answer→Question 181 Mark
Identify the like terms in the following algebraic expressions:
$a b c+a b^2 c+2 a c b^2+3 c^2 a b+b^2 a c-2 a^2 b c+3 c a b^2$
AnswerThe like terms in the given algebraic expressions are as follows:
The like terms in the given algebraic expressions are $a b^2 c, 2 a c b^2, b^2 a c$ and $3 c a b^2$.
View full question & answer→Question 191 Mark
Identify the monomials, binomials, trinomials and quadrinomials from the following expressions:
$a x^3+b x^2+c x+d$
AnswerThe quadrinomial are as follows:
$a x^3+b x^2+c x+d$ is a quadrinomial expression as it contains four terms.
View full question & answer→Question 201 Mark
Identify the monomials, binomials, trinomials and quadrinomials from the following expressions:
$a^2-b^2$
AnswerThe binomial are as follows:
$a^2-b^2$ is a binomial expression as it contains two terms.
View full question & answer→Question 211 Mark
Add the following:
3x and 7x
AnswerWe have,
3x + 7x
= (3 + 7)x
= 10x
View full question & answer→Question 221 Mark
Write the following statements by using appropriate grouping symbols:
The sum of a - b and 3a - 2b + 5 is subtracted from 4a + 2b - 7.
AnswerThe sum of a - b and 3a - 2b + 5
= [(a - b) + (3a - 2b + 5)]
This is subtracted from 4a + 2b - 7
Thus, the required expression is (4a + 2b - 7) - [(a - b) + (3a - 2b + 5)]
View full question & answer→Question 231 Mark
Write the coefficient of x in the following:-7xy
AnswerThe coefficients of x are as follows:
The numerical coefficient of x is -7y.
View full question & answer→Question 241 Mark
Write the numerical coefficient of the following:
7abc
AnswerThe numerical coefficient of the given terms is as follows:
The numerical coefficient in the term 7abc is 7.
View full question & answer→Question 251 Mark
Simplify the following:
$7 x^3 y+9 y x^3$
AnswerSimplifying the given expressions,
We have,
$7 x^3 y+9 y x^3$
$=(7+9) x^3 y$
$=16 x^3 y$
View full question & answer→Question 261 Mark
Write the coefficient of:
z in -7xyz
AnswerThe coefficients are as follows:
The coefficient of z is -7xy.
View full question & answer→Question 271 Mark
Write the constant term of the following algebraic expressions:
$a^3-3 a^2+7 a+5$
AnswerThe constant term of the given algebraic expressions is as follows:
The constant term in the given algebraic expressions is 5 .
View full question & answer→Question 281 Mark
Identify the monomials, binomials, trinomials and quadrinomials from the following expressions:
2x - 3y + 4
AnswerThe trinomial are as follows:
2x - 3y + 4 is a trinomial expression as it contains three terms.
View full question & answer→Question 291 Mark
Write all the terms of the following algebraic expressions:
$2 x^2+y^2-3 x y+4$
AnswerThe terms of the given algebraic expressions are as follows:
$2 x^2, y^2,-3 x y$ and 4 are the terms of the given algebraic expression.
View full question & answer→Question 301 Mark
Write the coefficient of:
p in -3pqr
AnswerThe coefficients are as follows:
The coefficient of p is -3pr.
View full question & answer→Question 311 Mark
Write the coefficient of:
$x^2 \text { in }-x^2$
AnswerThe coefficients are as follows:
The coefficient of $-x^2$ is -1 .
View full question & answer→Question 321 Mark
Place the last two terms of the following expressions in parentheses preceded by a minus sign:
x + y - 3z + y
AnswerWe have,
x + y - 3z + y
= x + y - (3z - y)
View full question & answer→Question 331 Mark
Identify the monomials, binomials, trinomials and quadrinomials from the following expressions:
xy + yz + zx
AnswerThe trinomial are as follows:
xy + yz + zx is a trinomial expression as it contains three terms.
View full question & answer→Question 341 Mark
AnswerRequired expression:
= -3xy - 4xy
= -7xy
View full question & answer→Question 351 Mark
Write the numerical coefficient of the following:
$-2 x^3 y^2 z$
AnswerThe numerical coefficient of the given terms is as follows:
The numerical coefficient in the term $-2 x^3 y^2 z$ is -2.
View full question & answer→Question 361 Mark
Write the numerical coefficient term in the following algebraic expressions:
$4\text{x}^2\text{y}-\frac32\text{xy}+\frac52\text{xy}^2$
AnswerThe numerical coefficient term in the given algebraic expression is as follows.
| Term |
Coefficient |
| $\text{4x}^2\text{y}$ |
$4$ |
| $-\frac32\text{xy}$ |
$-\frac32$ |
| $\frac{5}{2}\text{xy}^2$ |
$\frac52$ |
View full question & answer→Question 371 Mark
Identify the terms and also mention the numerical coefficients of those terms: $4 x y,-5 x^2 y,-3 y x, 2 x y^2$
Answer
|
Like terms
|
Numerical coefficients
|
|
-4xy, -3yx
|
-4, -3
|
View full question & answer→Question 381 Mark
Evaluate the following algebraic expressions for x = 1, y = -1, z = 2, a = -2, b = 1, c = -2:
ax + by + cz
AnswerWe have x = 1, y = -1, z = 2, a = -2, b = 1 and c = -2.
Thus,
ax + by + cz
= (-2)(1) + (1)(-1) + (-2)(2)
= -2 - 1 - 4
= -7
View full question & answer→Question 391 Mark
Write the coefficient of:
$y^2 \text { in } 9 x y^2 z$
AnswerThe coefficients are as follows:
The coefficient of $y^2$ is $9 x z$.
View full question & answer→Question 401 Mark
Write the coefficient of:
a in 2ab
AnswerThe coefficients are as follows:
The coefficient of a is 2ab.
View full question & answer→Question 411 Mark
Write the numerical coefficient of the following:
xy
AnswerThe numerical coefficient of the given terms is as follows:
The numerical coefficient in the term xy is 1.
View full question & answer→Question 421 Mark
Add the following:
-5xy and 9xy
AnswerWe have,
-5xy + 9xy
= (-5 + 9)xy
= 4xy
View full question & answer→Question 431 Mark
Identify the monomials, binomials, trinomials and quadrinomials from the following expressions:abc + 1
AnswerThe binomial are as follows:
abc + 1 is a binomial expression as it contains two terms.
View full question & answer→Question 441 Mark
Write the coefficient of 2 in the following: $-\frac32\text{ax}^2+\text{yx}$
AnswerThe coefficient of $x^2$ is as follows: The numerical coefficient of $x^2$ is $-\frac32\text{a}.$
View full question & answer→Question 451 Mark
Identify the monomials, binomials, trinomials and quadrinomials from the following expressions:3x - 2 + 5
AnswerThe binomial are as follows:
3x - 2 + 5 = 3x + 3 is a binomial expression as it contains two terms.
View full question & answer→Question 461 Mark
Write the coefficient of x in the following:xyz
AnswerThe coefficients of x are as follows:
The numerical coefficient of x is yz.
View full question & answer→Question 471 Mark
AnswerRequired expression:
= (-5y) - (-2x)
= -5y + 2x
View full question & answer→Question 481 Mark
Write 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 $9 x^2-3 y^2-x y$.
AnswerThe product of subtraction of $x^2-y^2+4 x y$ from $2 x^2+y^2-3 x y$ is given by $\left[\left(2 x^2+y^2-3 x y\right)-\left(x^2-y^2+4 x y\right)\right]$
When the above equation is added to $9 x^2-3 y^2-x y$, we get
$\left[\left(2 x^2+y^2-3 x y\right)-\left(x^2-y^2+4 x y\right)\right]+\left(9 x^2-3 y^2-x y\right)$
View full question & answer→Question 491 Mark
Place the last two terms of the following expressions in parentheses preceded by a minus sign:
7a + 3b + 2c + 4
AnswerWe have,
7a + 3b + 2c + 4
= 7a + 3b - (-2c - 4)
View full question & answer→Question 501 Mark
Place the last two terms of the following expressions in parentheses preceded by a minus sign:
3a - 2b + 4c - 5
AnswerWe have,
3a - 2b + 4c - 5
= 3a - 2b - (-4c + 5)
View full question & answer→