Expanding & Factorising Brackets (Cambridge (CIE) IGCSE Maths: Extended): Non-Calculator Questions

Factorise completely  $21a^2+28ab.$

Expand and simplify.

$\left(m-3\right)\left(m+2\right)$

Expand and simplify $(x+3)(x+5)$.

Expand and simplify.

$(3x-7)(2x+9)$

Expand.

$2x(3-x^2)$

Expand and simplify.

$6(2y-3)-5(y+1)$

Expand the brackets and simplify.

$(2p+3)(3p-2)$

Factorise completely $15k^{2}m-20m^4$.

Expand and simplify.

$x(x+2)(x–3)$

Factorise $6x^2+7x-20$.

Factorise $3x+8y-6ax-16ay$.

$x^2-12x+a={\left(x+b\right)}^2$
Find the value of $a$ and the value of $b$.

   $a=$ .................................................

$b=$ .................................................

Factorise.

$xy-2x+3y-6$

Expand and simplify $(x+1)(x+2)+2x(x-3)$.

Factorise $p^2-q^2$ .

$p^2-q^2=7$ and $p-q=2$.

Find the value of $p+q$.

Complete this statement with an expression in terms of $m$.

 $18m^3+9m^2+14m+7=(9m^2+7)(..............................)$ 

Factorise.

$xy+5y+2x+10$

Factorise completely.

$px+py-x-y$

Factorise completely.

$xy+2y+3x+6$

Factorise completely.

$2a+4b-ax-2bx$

Factorise completely  $20x^2-45y^2.$

Expand and simplify  $(x+3)(x-5)(3x-1).$

Factorise.

$18y-3ay+12x-2ax$

Factorise.

$3x^2-48y^2$

Factorise $12(m+p)+8{\left(m+p\right)}^2$.