Factorisation of Polynomials

Factorise the polynomial $4x^4+12x^3+8x^2$ and divide it by $4x^2$

Solve the following quadratic equation.

$1-27y^3=(1-3y)(1+3y-9y^2)$

 Expand the given expression:
$(1-x{)}^3$

 Prove the following equation:

$x^3+64=(x+4)(x^2-4x+16)$

Factorise

$64x^3+125y^3+12x^{2}y+15x{y}^2$

Which of the following is the factorised form of $ {\left(x+y\right)}^{2}-1$ ?

Which of the following identities is most useful in factorising this expression, $ {\left(x+y\right)}^{3}-x-y$ ?

Which of the following expressions is the same as $ 4{m}^{2}-2m-25{n}^{2}-5n$ ?

Find the value of the expression using algebraic identities:

${\left(201\right)}^{3 }$

Expand the following expression:

${\left({\mathrm{x}}^2+\mathrm{y}\right)}^{3 }$

Factorise the following by splitting the middle term.
$a^2-16a-80$

Factorise the following by splitting the middle term.
$z^2-13z-30$

Factorise the following by splitting the middle term.
$b^2-10b+21$

Factorise the following by splitting the middle term.
$z^2+11z+18$

Factorise the following by splitting the middle term.
$y^2-2y-15$

Factorise the following by splitting the middle term.
$s^2+4s-21$

Factorise the following by splitting the middle term.
$z^2+18z+65$

Factorise the following by splitting the middle term.
$a^2+15a+26$

The area of a rectangular lawn is equal to $x^2+12x+35$ sq.m. Find the length and breadth of the rectangular lawn. If the cost of fencing this lawn with wires is $₹ 3,000$ at the rate of $₹ 25$ per meter, then find out the value of $x$ and hence the actual dimension of the rectangular lawn.

The reduced form of ( $36x^2-81y^2$) is