A K Upadhyay and S Upadhyay Solutions for Chapter: Polynomials, Exercise 5: EXERCISE 2.5

Find the value of $8a^3+27b^3+125-90ab$ when $2a=-(5+3b)$

If $a+b+c=5$ and $ab+bc+ca=10$ then prove that $a^3+b^3+c^3-3abc=-25$

If $p=2-a$, then prove that $a^3+6ap+p^3-8=0$

The volume of a cube is given by the polynomial $P\left(x\right)=8x^3-36x^2+54x-27$. Find the possible expression for the side of the cube. Verify it when side of the cube is $3 \mathrm{cm}$.

Factorize $a^{12}{x}^4-a^4{x}^{12}$.

Find the value of $x^3-8y^3-36xy-216$ when $x=2y+6$

If $p=4-q$, prove that $p^3+q^3+12pq=64$

Factorize ${\left(x-2y\right)}^3+{\left(2y-3z\right)}^3+{\left(3z-x\right)}^3.$