Expansion of (a ± b)³

Q.

Without actually calculating the cubes, find he value of the following: ${\left(28\right)}^3$ + ${(-15)}^3$ + ${(-13)}^3$

Q.

Evaluate ${\left(998\right)}^3$ by using suitable identity?

Q. If. (a + 1/a) whole square =3. ; a is not equal to 0

Show that: a cube + 1/a cube = 0

Q. If $a^2+\frac{1}{a^2}=34$, then the value of $a^3+\frac{1}{a^3}$ is equal to.

1. $\pm 234$
2. $98$
3. $\pm 198$
4. $\pm 99$

Q.

a+b=10, a square+b square =58. Find a cube+b cube

Q.

If $a+b-12=0$ and $ab=27$, then find the value of $a^3+b^3$.

Q. The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their squares.

1. 30
2. 41
3. 29
4. 49

Q.

Write the following cubes in expanded form: (x - $\frac{2y}{3}{)}^3$

Q.

Multiply cube root of 8 by square root of 5.

Q.

Question 34
Factorise:
(i) $1+64x^3$

(ii) $a^3-2\sqrt{2}{b}^3$

Q. Question 37
Without actually calculating the cubes, find the value of
(i) ${\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{3}\right)}^3-{\left(\frac{5}{6}\right)}^3$

(ii) $(0.2{)}^3-(0.3{)}^3+(0.1{)}^3$

Q.

Write the following cubes in expanded form: ${(2x+1)}^3$

Q. If 3a + 5b + 4c = 0; then the value of 27a³ + 125b³ + 64c³
is

1. 160abc
2. 240abc
3. 200abc
4. 180abc

Q.

Cube of 45 is

1. 37125

2. 37005

3. 90005

4. 91125

Q. If the sum of three numbers be 9 the sum of their squares be 29 and their sum of cubes be 99 then find the product

Q.

Write the following cubes in expanded form:

($\frac{3x}{2}+1{)}^3$

Q. If S is the set of all the real X such that 2x - 1 by 2 x cube + 3 X square + X is positive then S contains

Q. Evaluate the following:

(iv) ${93}^3-{107}^3$

Q. If a2+b2=23ab show that:
log a+b÷5=1÷2(log a+log b)

Q. Find the cube of 3a - 2b .

1. $27a^3-54b^3-8a^{2}b+36a{b}^2$
2. $27a^3-8b^3-54a^{2}b+36a{b}^2$
3. $27a^3-8b^3-54a^{2}b-36a{b}^2$
4. $27a^3+8b^3+54a^{2}b+36a{b}^2$

Q. Evaluate the following:

(iii) ${104}^3+{96}^3$

Q. How to find the value of log 3 X 10^5

Q. Find the cube of $2a+\frac{1}{2a}$ ( $a\ne$0) .

1. $16a^3-\frac{1}{8a^3}+6a-\frac{8}{2a}$
2. $4a^3+\frac{1}{4a^3}+4a+\frac{8}{2a}$
3. $8a^3+\frac{1}{8a^3}+6a+\frac{3}{2a}$
4. $8a^3-\frac{1}{8a^3}-6a-\frac{3}{2a}$

Q.

If the sum of 2 numbers is 11 and the sum of their cubes is 737.

Find the sum of their squares

Q. Question 14
Without actually calculating the cubes, find the value of each of the following:
$\left(i\right)(-12{)}^3+(7{)}^3+(5{)}^3$
$\left(ii\right)(28{)}^3+(-15{)}^3+(-13{)}^3$

Q.

Write the following cubes in expanded form:

(i) $(2x+1{)}^3$

(ii)$(2a-3b{)}^3$

(iii) $(\frac{3}{2}x+1{)}^3$

(iv) $(x-\frac{2}{3}y{)}^3$

Q. Find the cube of $2a+\frac{1}{2a}$ ( $a\ne$0) .

1. $4a^3+\frac{1}{4a^3}+4a+\frac{8}{2a}$
2. $8a^3-\frac{1}{8a^3}-6a-\frac{3}{2a}$
3. $8a^3+\frac{1}{8a^3}+6a+\frac{3}{2a}$
4. $16a^3-\frac{1}{8a^3}+6a-\frac{8}{2a}$

Q. Subtract (4x(quartic)-2x(cube)-6x(square)+x-5)-(ax+b)

Q. Cube of $a-2b$ is _______.

1. $a^3-8b^3-6a^{2}b+12a{b}^2$
2. $a^3+8b^3-6a^{2}b+12a{b}^2$
3. $8a^3-18b^3-6a^{2}b+12a{b}^2$
4. $a^3+8b^3+6a^{2}b+12a{b}^2$

Q. Question 6
Write the following cubes in expanded form:

$\left(i\right)(2x+1{)}^3(ii\left)\right(2a-3b{)}^3\left(iii\right){[\frac{3}{2}x+1]}^3\left(iv\right){[x-\frac{2}{3}y]}^3$