R S Aggarwal and Veena Aggarwal Solutions for Exercise 6: EXERCISE 3F

Factorize: $a^{12}-b^{12}$. If the answer is $k\left(a-b\right)\left(a^2+b^2\right)\left(a^4-a^2{b}^2+b^4\right)\left(a^4+a^2{b}^2+b^4\right)$, find $k$.

Factorize: $x^6-7x^3-8$. If the answer is $k(x+1)\left(x^2-x+1\right)\left(x^2+2x+4\right)$, find $k$.

Factorize: $x^3-3x^2+3x+7$. If the answer is $k\left(x^2-4x+7\right)$, find $k$.

Factorize: $(x+1{)}^3+(x-1{)}^3$. If the answer is $k\left(x^2+3\right)$, find the value of $k$.

Factorize: $(2a+1{)}^3+(a-1{)}^3$. If the answer is $k\left(a^2+a+1\right)$, find $k$.

Factorize: $8(x+y{)}^3-27(x-y{)}^3$. If the answer is $k\left(19x^2+7y^2-10xy\right)$, find $k$.

Factorize: $(x+2{)}^3+(x-2{)}^3$. If the answer is $k\left(x^2+12\right)$, find $k$.

If $(x+2{)}^3-(x-2{)}^3=4\left(k{x}^2+4\right)$, then find the value of $k$.