FACTORIZING ALGEBRAIC EXPRESSIONS

Factorise: 3x+6

• 2(x+3)

• 3(x+2)

• 6(3x+1)

• 6(x+1)

Factorize: 2p+4q+6r

• p(2+4q+6r)

• 2p(1+2q+3r)

• 2(p+2q+3r)

• 2(1+2q+3r)

Factorise as fully as possible: 3xy+3x

• 3x(y+1)

• 3(xy+x)

• x(3y+3)

Factorise as fully as possible: $90m^3-80m^2$  

•  $10\left(9m^3-8m^2\right)$  

•  $10m\left(9m^2-8m\right)$  

•  $5m^2\left(18m-16\right)$  

•  $10m^2\left(9m-8\right)$  

Factorise as fully as possible: $32p^2q-4pq^2$  

•  $8pq\left(4p-\frac{p}{2}\right)$  

•  $4pq\left(8p-q\right)$  

•  $pq\left(32p-4q\right)$  

•  $4\left(8p^2q-pq^2\right)$  

Factorise as fully as possible: $m^3n^2+6m^2n^2\left(8m+n\right)$  

•  $mn\left(m^2n+6mn+8m+1\right)$  

•  $m^2\left(mn^2+48n^2m+6n^3\right)$  

•  $m^2n^2\left(m+48mn+6n\right)$  

•  $m^2n^2\left(49m+6n\right)$  

Factorise as fully as possible: $\frac{1}{2}a+\frac{3}{2}b$  

•  $\frac{1}{2}\left(a+3b\right)$  

•  $2\left(\frac{a}{4}+6b\right)$  

•  $\frac{a+3b}{2}$  

Factorise as fully as possible: $\frac{3}{4}x^4+\frac{7}{8}x$  

•  $x\left(\frac{3}{4}x^3+\frac{7}{8}\right)$  

•  $\frac{1}{4}\left(3x^4+\frac{7}{2}x\right)$  

•  $\frac{x}{2}\left(\frac{3x^2}{2}+\frac{7}{4}\right)$  

•  $\frac{x}{4}\left(3x^3+\frac{7}{2}\right)$  

Factorise as fully as possible: $5\left(x+1\right)^2-4\left(x+1\right)^3$  

•  $\left(x+1\right)\left(-4x^2-3x+1\right)$  

•  $\left(x+1\right)^2\left(1-4x\right)$  

•  $-4x^3-7x^2-2x+1$  

•  $\left(x+1\right)^2\left(9-4x\right)$  

Factorise as fully as possible: $7x^3y-14x^2y^2+21xy^2$  

•  $7\left(x^3y-2x^2y^2+3xy^2\right)$  

•  $x^2y\left(7x-14y+21y\right)$  

•  $7xy^2\left(x^2-2x+3y\right)$  

•  $7xy\left(x^2-xy+3y\right)$