Expansion of (x+y)^3

Q.

Find $a^3+\frac{1}{a^3}ifa+\frac{1}{a}=5$

Q.

If a + b = 8 and ab = 15, find : $a^3+b^3$.

Q. If $a-\frac{1}{a}=3$; find $a^3-\frac{1}{a^3}$.

1. $18$
2. $24$
3. $36$
4. $27$

Q.

If a + b = 6 and ab = 8; find $a^3+b^3$

Q.

If $3x+\frac{1}{3x}=3;find:\left(i\right)9x^2+\frac{1}{9x^2}\left(ii\right)27x^3+\frac{1}{27x^3}$

Q.

What is the value of $a^3-b^3$ ?

1. $(a-b)(a^2+b^2+ab)$

2. $(a+b)(a^2+3b^2-2ab)$

3. $(a+b)(2a^2+b^2-ab)$

4. $(a-b)(a^2+b^2-ab)$

Q.

If $3x+2y=9andxy=3,find:27x^3+8y^3$

Q.

If (a+ b) = 7 and ab = 8 find $a^3+b^3$

1. -175

2. 175

3. 7

4. 125

Q.

If $x+\frac{1}{x}=11$ , then find $x^3+\frac{1}{x^3}$

1. 121

2. 1298

3. 1331

4. 1364

Q.

If $(8a^3+27b^3)=0$

then

$(4a^2+9b^2)=$

1. $0$

2. $6ab$

3. $18ab$

4. $-6ab$

Q. Find and correct the errors in the statement: $(2x{)}^2+5x=4x+5x=9x$

Q.

The value of $(2x+3y{)}^3$ is __________.

1. $8x^3$ + $27y^3$ +$36x^{2}y$ + $54x{y}^2$

2. $8x^3$ + $27y^2$ +$36x^{2}y$ + $54x{y}^2$

3. $8x^3$ + $27y^3$ +$36x^{3}y$ + $54x{y}^2$

4. $8x^3$ + $27y^3$ +$36x^{2}y$ + $54x{y}^3$

Q.

If $x-\frac{1}{x}$ = 9 then $x^3-\frac{1}{x^3}$ = _____________

1. 756

2. 702

3. 740

4. 729

Q.

"Three times $x$ added to the cube of $y$" is

1. $3(x+y^3)$

2. $3x{y}^3$

3. $3x+y^3$

4. $3(x+3y)$

Q. $16-a^6+4a^3{b}^3-{ab}^6$

Q. Question 3(vi)
Find the following squares by using identities:
$(2xy+5y{)}^2$

Q. If $(a+\frac{1}{a})=12$, then $(a^3+\frac{1}{a^3})$ is equal to:-

1. $1680$
2. $1686$
3. $1698$
4. $1692$

Q. Question 3(ii)
Find the following squares by using identities:
$(xy+3z{)}^2$

Q. State True or False.

1. True
2. False

Q. If $(y+\frac{1}{y})=12$, then $(y^3+\frac{1}{y^3})$ is equal to:-

1. $1680$
2. $1686$
3. $1692$
4. $1698$

Q. $[3a^2-2a^2+9a^2-\{6a^2-\left(-2a^2+3a^2\right)\left\}\right]$

Q.

If x + y = 5 and xy = 6

then

x^3 + y^3 =

1. 90

2. 125

3. 25

4. 35

Q. Find and correct the errors in the statement: $(2x{)}^2+5x=4x+5x=9x$

Q. If $\omega$ is a complex cube root of unity with $\omega \ne 1$ and $p=\left[p_{ij}\right]$ is a $n\times n$ matrix with $p_{ij}={\omega }^{i+j}$. Then, $p^2\ne 0$, when $n$ is equal to

1. $57$
2. $55$
3. $58$
4. $56$

Q.

If a + b = 2 , then the sum of (a + b) and the cube of (a+b) is ___

1. Charlie's Dad

2. Kim

3. Jen

4. Charlie

Q.

If a + b = 9 ; then the cube of (a + b) =

1. -210

2. 234

3. -234

4. 210