Algebraic Identity (a+b)^3

Q.

Find the cube of $x+2y$.

1. $x^3+8y^3+6x^{2}y+12x{y}^2$

2. $x^3+8y^3+6x^{2}y-12x{y}^2$

3. $x^3+8y^3+12x^{2}y+6x{y}^2$

4. $x^3+8y^3-6x^{2}y+12x{y}^2$

Q.

Using special products, simplify :

${(2x-3y)}^2$

Q.

If $a+\frac{1}{a}=3$, then find the value of $(a^2+\frac{1}{a^2})(a^3+\frac{1}{a^3})$

1. 112

2. 123

3. 125

4. 126

Q.

Find the cube of $x+\frac{1}{x}$

1. $x^3+\frac{1}{x^3}+3x+\frac{3}{x}$

2. $x^3+\frac{1}{x^3}+3x+\frac{3}{x^2}$

3. $x^3+\frac{1}{x^3}+3x^2+\frac{3}{x}$

4. $x^3+\frac{1}{x^3}+3x^2+\frac{3}{x^2}$

Q. Expand $(7x-9y{)}^3$ [3 marks]

Q.

$(a+b{)}^3-(a-b{)}^3$ =________

1. $b^3+3a^{2}b$

2. $2(b^3+3a^{2}b)$

3. $2(a^3+3a{b}^2)$

4. 0

Q.

The cube of $xy-\frac{1}{(xy{)}^2}=$

1. $x^3{y}^3-\frac{1}{x^6{y}^6}-3+\frac{3}{xy}$

2. $x^3{y}^3-\frac{1}{x^6{y}^6}-3+\frac{3}{x^2{y}^2}$

3. $x^3{y}^3-\frac{1}{x^6{y}^6}-3+\frac{3}{x^3{y}^3}$

4. $x^3{y}^3-\frac{1}{x^3{y}^3}-3+\frac{3}{x^3{y}^3}$

Q.

Find the product of $(2x-3y)$ and $(4x^2+9y^2+6xy)$.

1. $8x^3-27y^3$

2. $2x^3-3y^3$

3. $(2x-3y{)}^3$

4. $(8x-27y{)}^3$

Q. Expand the following:
$(1+2x{)}^3$

Q. Evaluate the product of $(\sqrt{7}x+\sqrt{5})(\sqrt{5}x+\sqrt{7})$

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

4. $18x^3+27y^3+36x^{2}y+54x{y}^2$

Q. If $x=-2$ and $y=1,$ by using an identity find the value of the following:

$\left(i\right)$ $(4y^2-9x^2)(16y^4+36x^2{y}^2+81x^4)$

Q. Find the cube of :
$(2x+\frac{1}{x})$

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

Q.

The power of $x$ in $2x{y}^3$

Q.

Expand the following identity.
​${(2x+1)}^3$

1. ${8x}^3-1+12x^2+6x$

2. ${8x}^3-1-12x^2+6x$

3. ${8x}^3+1+12x^2+6x$

4. ${8x}^3+1+12x^2-6x$

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. Find the cube of 5a+3b .

1. $125a^3-225a^{2}b-135a{b}^2-27b^3$
2. $125a^3+27b^3+225a^{2}b+135a{b}^2$
3. $125a^3+125a^{2}b+135a{b}^2-27b^3$
4. $125a^3-225a^{2}b-135a{b}^2-27b^3$

Q.

Find the cube of $x+2y$.

1. $x^3+8y^3+6x^{2}y+12x{y}^2$

2. $x^3+8y^3+6x^{2}y-12x{y}^2$

3. $x^3+8y^3+12x^{2}y+6x{y}^2$

4. $x^3+8y^3-6x^{2}y+12x{y}^2$

Q.

If $a+\frac{1}{a}=3$, then find the value of $(a^2+\frac{1}{a^2})(a^3+\frac{1}{a^3})$

1. 123

2. 125

3. 126

4. 112

Q. If m is the successor of n, find the value of ${\left(n+m\right)}^2$, where both n, m are positive integers.

1. $4n^2+4n-1$
2. $4n^2-4n+1$
3. $4n^2+4n+1$
4. $4n^2-4n-1$