Sample QuestionsAlgebraic Expressions and Identities questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If we subtract $4a - 7ab + 3b + 12$ from $12a - 9ab + 5b - 3,$ then the answer is:
- ✓
$8a - 2ab + 2b - 15$
- B
$8a + 2ab + 2b - 15$
- C
$8a - 2ab - 2b - 15$
- D
$8a + 2ab + 2b + 15$
Answer: A.
View full solution →If we multiply $5x$ and $(-4xyz),$ then we get:
- A
$20x^2yz$
- ✓
$-20x^2yz$
- C
$x^2yz$
- D
$-2xyz$
Answer: B.
View full solution →Tick $(\checkmark)$ the correct answer: $(x + 5)(x - 3) = ?$
- A
$x^2 + 5x - 15$
- B
$x^2 - 3x - 15$
- C
$x^2 + 2x + 15$
- ✓
$x^2 + 2x - 15$
Answer: D.
View full solution →Which are the standard identities?
- A
$(a+b)^2=a^2+2 a b+b^2(a-b)^2=a^2-2 a b+b^2$ and $(x+a)(x+b)=x^2+(a-b) x+a b$
- B
$(a-b)^2=a^2-2 a b+b^2 a^2-b^2=(a+b)(a-b)$ and $(x+a)(x+b)=x^2+(a-b) x+a b$
- C
$(a+b)^2=a^2+2 a b+b^2 a^2-b^2=(a+b)(a-b)$ and $(x+a)(x+b)=x^2+(a-b) x+a b$
- ✓
$(a+b)^2=a^2+2 a b+b^2(a-b)^2 a^2 2 a b+b^2$ and $a^2-b^2=(a+b)(a-b)$
Answer: D.
View full solution →Which of the following is a trinomial?
- A
$-7z$
- B
$z^2- 4y^2$
- ✓
$x^2y - xy^2 + y^2$
- D
$12a - 9ab + 5b - 3$
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$: The number of like terms in $abc, -abc, -bca, acb, bac, 12cab$ is $4$
Reasons $(R)$: like terms are terms that have the same variables and powers
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$: The expression $x + 3$ is in one variable
Reasons $(R)$: The expression $(n + 3)$ represents the measure of an exterior angle of a regular octadecagon
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- ✓
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$: $1$ term is there in the expression $5xy^2$
Reasons $(R)$: An algebraic expression consists of a group of terms separated by operators, which are either plus signs or minus signs
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$: The coefficient in the term $-5x$ is $5$
Reasons $(R)$: A coefficient is a number multiplied by a variable
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$: The value of $x^2+ y^2$ when $x = 1, y = 2$ is $5$.
Reasons $(R)$: a numerical coefficient is defined as a fixed number that is multiplied to a variable
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
Answer: A.
View full solution →Simplify: $(a + b + c)(a + b - c)$
View full solution →Simplify: $(1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12y.$
View full solution →Simplify: $(x + y) (2x + y) + (x + 2y) (x - y)$
View full solution →Simplify: $(a + b)(c - d) + (a - b)(c + d) + 2(ac + bd)$
View full solution →Simplify: $(a^2+ 5) (b^3+ 3) + 5$
View full solution →Simplify $3x (4x – 5) + 3$ and find its values for $x = \frac{1}{2}$
View full solution →Complete the table of products.
| $\frac{\text { First monomial } \rightarrow}{\text { Second monomial } \downarrow}$ |
$2x$ |
$-5y$ |
$3x^2$ |
$-4xy$ |
$7x^2y$ |
$-9x^2y^2$ |
| $2x$ |
$4x^2$ |
- |
- |
- |
- |
- |
| $-5y$ |
- |
- |
$-15x^2y$ |
- |
- |
- |
| $3x^2$ |
- |
- |
- |
- |
- |
- |
| $-4xy$ |
- |
- |
- |
- |
- |
- |
| $7x^2y$ |
- |
- |
- |
- |
- |
- |
| $-9x^2y^2$ |
- |
- |
- |
- |
- |
- |
View full solution →Subtract: $3pq(p – q)$ from $2pq(p + q).$
View full solution →Find the volume of each rectangular box with given length, breadth and height.
| |
Length |
Breadth |
Height |
| $1$ |
$2ax$ |
$3by$ |
$5cz$ |
| $2$ |
$m^2n$ |
$n^2p$ |
$p^2m$ |
| $3$ |
$2q$ |
$4q^2$ |
$8q^3$ |
View full solution →Simplify:$(x+y)\left(x^2-x y+y^2\right)$
View full solution →Simplify: $\left(t+s^2\right)\left(t^2-s\right)$
View full solution →Find the product: $\left(p^{2}-q^{2}\right)(2 p+q)$
View full solution →Find the product of $\left(a^2+b\right)$ and $\left(a+b^2\right)$
View full solution →Find the product: $(x + 7y)(7x - y)$
View full solution →$2 x^2-2 x+3$ is a _______ expression. (monomial, binomial, trinomial)
View full solution →$2x-3x y-x$ is a _______ expression. (monomial, binomial, trinomial)
View full solution →The numerical coefficient of the term $\left(-4 x^3 y^2\right)$ is _______ . $[2, 3, (-4)]$
View full solution →The number of terms in the expression $5 x^3-4 x^2+3$ is _______ . (one, two, three)
View full solution →$8 x^4-6 x y$ is a _______ expression. (monomial, binomial, trinomial)
View full solution →