Algebraic Identities

Simplify: ${\left(7x+y\right)}^3-{\left(7x-y\right)}^3$

On simplification $(3+\sqrt{3})(3-\sqrt{3})$ gives:

Find the product, using suitable identity:

$\left(a-\frac{1}{a}\right)\left(a+\frac{1}{a}\right)\left(a^2+\frac{1}{a^2}\right)\left(a^4+\frac{1}{a^4}\right)$

The value of ${\left(a^2-b^2\right)}^3+{\left(b^2-c^2\right)}^3+{\left(c^2-a^2\right)}^3$ is 

Simplify, $12(y^2+7y{)}^2-8(y^2+7y\left)\right(2y-1)-15(2y-1{)}^2$

If $x+y=8, xy=15$, then find the value of $x^4+x^2{y}^2+y^4$

Find the value of $\frac{(237+12{)}^2-(237-12{)}^2}{237\times 12}$

The value of $(a^2-b^2{)}^3+(b^2-c^2{)}^3+(c^2-a^2{)}^3$ if $a+b+c=0$ is 

If $M=5+5^{\frac{1}{3}}+5^{\frac{2}{3}}$, then the value of $M^3-15M^2+60M-40$ is

Solve the following questions with suitable identities: 

$104\times 96$

Solve the following questions with suitable identities: 

$103\times 107$

Solve the following questions with suitable identities: 

$105\times 106$

Solve: ${\left(999\right)}^3$

Solve: ${\left(998\right)}^3$

Solve: ${\left(102\right)}^3$

Solve: ${\left(104\right)}^3$

Solve the following question with suitable identity: $105\times 95$

Solve the following questions with suitable identities: 

$\left(100+4\right)\left(100-4\right)$

Solve the following question with suitable identities: $95\times 97$

Solve the following questions with suitable identities: 

$104\times 96$