Which of the following expressions are polynomials in one variable and which are not ? State reasons for your answer. $3 \sqrt{t}+t \sqrt{2}$
$3 \sqrt{t}+t \sqrt{2}$
$\Rightarrow 3 t^{1 / 2}+\sqrt{2} \cdot t$
$\because $ $\frac{1}{2}$ is not a whole number,
$\therefore $ $3 t^{1 / 2}+\sqrt{2} \cdot t,$ i.e. $3 \sqrt{t}+t \cdot \sqrt{2}$ is not a polynomial.
Factorise of the following : $27-125 a^{3}-135 a+225 a^{2}$
Find the degree of the polynomials given : $2-y^{2}-y^{3}+2 y^{8}$
Use suitable identities to find the products : $\left(y^{2}+\frac{3}{2}\right)\left(y^{2}-\frac{3}{2}\right)$
Expand each of the following, using suitable identities : $\left[\frac{1}{4} a-\frac{1}{2} b+1\right]^{2}$
Without actually calculating the cubes, find the value of each of the following : $(28)^{3}+(-15)^{3}+(-13)^{3}$