Use suitable identities to find the products : $\left(y^{2}+\frac{3}{2}\right)\left(y^{2}-\frac{3}{2}\right)$
$\left(y^{2}+\frac{3}{2}\right)\left(y^{2}-\frac{3}{2}\right)$
Using the identity $(a+b)(a-b)=a^{2}-b^{2},$ we have :
$\left(y^{2}+\frac{3}{2}\right)\left(y^{2}-\frac{3}{2}\right)=\left[y^{2}\right]^{2}-\left[\frac{3}{2}\right]^{2}=y^{4}-\frac{9}{4}$
Factorise : $4 x^{2}+9 y^{2}+16 z^{2}+12 x y-24 y z-16 x z$
Write the coefficients of $x^2$ in each of the following :
$(i)$ $2+x^{2}+x $
$(ii)$ $2-x^{2}+x^{3}$
Find the value of each of the following polynomials at the indicated value of variables : $p(t)=4 t^{4}+5 t^{3}-t^{2}+6$ at $t=a$.
Expand each of the following, using suitable identities : $(-2 x+3 y+2 z)^{2}$
Write the following cubes in the expanded form : $(5 p-3 q)^{3}$