Sample QuestionsFactorization Of Algebraic Expressions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $(x+y)^3-(x-y)^3-6 y\left(x^2-y^2\right)=k y^2$, then $k=$
Answer: D.
View full solution →The expression $(a-b)^3+(b-c)^3+(c-a)^3$ can be factorized as:
Answer: B.
View full solution →The value of $\frac{(2.3)^3-0.027}{(2.3)^2+0.69+0.09},$ is:
Answer: A.
View full solution →The factors of $x^3-7 x+6$ are:
Answer: D.
View full solution →The expression $x^4+4$ can be factorized as:
- ✓
$\left(x^2+2 x+2\right)\left(x^2-2 x+2\right)$
- B
$\left(x^2+2 x+2\right)\left(x^2+2 x-2\right)$
- C
$\left(x^2-2 x-2\right)\left(x^2-2 x+2\right)$
- D
$\left(x^2+2\right)\left(x^2-2\right)$
Answer: A.
View full solution →Statement-1 (A): The value of $\frac{(0.027)^3-(0.023)^3}{(0.027)^2-(0.027)(0.023)+(0.023)^2}$ is 0.05
Statement-2 $(R): \quad a^3-b^3=(a-b)\left(a^2-a b-b^2\right)$
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Stateme
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statemen
- ✓
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: C.
View full solution →Statement-1 (A): If $a, b, c$ are all non-zero such that $a+b+c=0$, then $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{a b}=$
Statement-2 (R): If $a+b+c=9$ and $a^2+b^2+c^2=35$, then $a b+b c+c a=23$
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Stateme
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statemen
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: B.
View full solution →Statement-1 (A): If $a+b+c=5$ and $a b+b c+c a=10$, then $a^3+b^3+c^3-3 a b c=25$
Statement-2 (R): $a^3+b^3+c^3-3 a b c=(a+b+c)\left\{(a+b+c)^2-3(a b+b c+c a)\right\}$
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Stateme
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statemen
- C
Statement-1 is true, Statement-2 is false.
- ✓
Statement-1 is false, Statement-2 is true.
Answer: D.
View full solution →Statement-1 (A): If $3 x=a+b+c$,
then$
(x-a)^3+(x-b)^3+(x-c)^3=3(x-a)(x-b)
$
Statement-2 (R): If $a+b+c=0$, then $a^3+b^3+c^3=3 a b c$
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Stateme
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statemen
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): $(a-b)^3+(b-c)^3+(c-a)^3=3(a-b)(b-c)(c-a)$
Statement-2 (R): If $a+b+c=0$, then $a^3+b^3+c^3=3 a b c$
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Stateme
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statemen
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: A.
View full solution →The factorized form of $a^3+b^3+3 a b-1$ is _______________ .
View full solution →The factorized form of $\frac{1}{x y z}\left(x^2+y^2+z^2\right)+2\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)$ is _______________
View full solution →If $3 x-\frac{y}{5}=10$ and $x y=5$, then the value of $27 x^3-\frac{y^3}{125}$ is _______________
View full solution →The factorisation form of $a^4+b^4-a^2 b^2$ is _______________ .
View full solution →The polynomial, $x^6+64 y^6$ on factorisation gives _______________ .
View full solution →Write the value of $25^3 - 75^3+ 50^3.$
View full solution →Write the value of $\Big(\frac{1}{2}\Big)^3+\Big(\frac{1}{3}\Big)^3-\Big(\frac{5}{6}\Big)^3.$
View full solution →Write the value of $30^3 + 20^3 - 50^3.$
View full solution →Write the value of $48^3-30^3-18^3$.
View full solution →Factorize: $x^2-1-2 a-a^2$.
View full solution →Factorize: $\text{x}^2-\sqrt{3}\text{x}-6$
View full solution →Factorize:
$2(x+y)^2-9(x+y)-5$
View full solution → Factorize:
$\text{x}^2+2\sqrt{3}\text{x}-24$
View full solution →If $a+b+c=0$, then write the value of $a^3+b^3+c^3$.
View full solution →Factorize:
$a^3 x^3-3 a^2 b x^2+3 a b^2 x-b^3$
View full solution →Factorize: $6ab - b^2 + 12ac - 2bc$
View full solution →Factorize: $x^2 + y - xy - x$
View full solution →Find the value of $x^3+y^3-12 x y+64$, when $x+y=-4$
View full solution →Factorize: $a^2 + 4b^2 - 4ab - 4c^2$
View full solution →Factorize: $x^3 + x - 3x^2 - 3$
View full solution →Factorize: $\text{x}^2+\frac{12}{35}\text{x}+\frac{1}{35}$
View full solution →Factorize: $a^2 + 2ab + b^2 - c^2$
View full solution →Factorize: $a(a + b)^3 - 3a^2b(a + b)$
View full solution →Factorize: $\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)-4\Big(\text{x}+\frac{1}{\text{x}}\Big)+6$
View full solution →Factorize the following expressions: $\Big[\frac{\text{x}}{2}+\text{y}+\frac{\text{z}}{3}\Big]^3+\Big[\frac{\text{x}}{3}-\frac{2\text{y}}{3}+\text{z}\Big]^3+\Big[-\frac{5\text{x}}{6}-\frac{\text{y}}{3}-\frac{4\text{z}}{3}\Big]^3$
View full solution →