# Algebra - Factorising Expressions

a - answer    s - solution    v - video    d - discussion

## Question 1

Find the Highest/Greatest Common Factor (HCF/GCF) for the following terms

a) $4,6$a s v d
b) $14,35$a s v d
c) $33,44,55$a s v d
d) $x,x^2$a s v d
e) $y,y^3$a s v d
f) $z^2,z^5$a s v d
g) $f^3,f^7$a s v d
h) $x,2x$a s v d
i) $5y,8y$a s v d
j) $8u,11u$a s v d
k) $3,3x$a s v d
l) $4,4y$a s v d

## Question 2

Find the HCF/GCF for the following terms

a) $4w,6w$a s v d
b) $3x,9x$a s v d
c) $10p,25p$a s v d
d) $2d,2d^2$a s v d
e) $7y^2,7y^3$a s v d
f) $8x,12x^2$a s v d
g) $6s,12s^2$a s v d
h) $20e^2,30e^3$a s v d
i) $12c^3,16c^4$a s v d
j) $27v^5,45v^8$a s v d
k) $16y^4,48y^{10}$a s v d
l) $34q^{14},51q^{22}$a s v d

## Question 3

Find the HCF/GCF for the following terms

a) $xy,xz$a s v d
b) $abcd,ac$a s v d
c) $tu,3tuv$a s v d
d) $4rt,4r$a s v d
e) $2e^2p,2ep$a s v d
f) $5xy,10xyz$a s v d
g) $12t^2u^3,20tu$a s v d
h) $10x^2y,15xy^2$a s v d
i) $4abc,6a^2b^2c^2$a s v d
j) $6f^2gh^3,10fg^2h$a s v d
k) $30p^3qr^5,45p^2q^2r$a s v d
l) $57a^7b^2c^3d^5,95a^5b^2c^5d$a s v d

## Question 4

By finding the HCF/GCF, fully factorise the following expressions

a) $2x+4$a s v d
b) $3x+9$a s v d
c) $5y+20$a s v d
d) $7z+21$a s v d
e) $8r+64$a s v d
f) $3t+33$a s v d
g) $3x-6$a s v d
h) $4y-12$a s v d
i) $2d-10$a s v d
j) $4h-20$a s v d
k) $10u-100$a s v d
l) $15q-75$a s v d

## Question 5

Fully factorise the following expressions

a) $4x+6$a s v d
b) $8y+20$a s v d
c) $12z+30$a s v d
d) $27s+45$a s v d
e) $15e+35$a s v d
f) $24t+56$a s v d
g) $6u-9$a s v d
h) $4r-10$a s v d
i) $10j-25$a s v d
j) $21q-28$a s v d
k) $30f-54$a s v d
l) $42r-70$a s v d

## Question 6

Fully factorise the following expressions

a) $x^2+2x$a s v d
b) $y^2+4y$a s v d
c) $z^2-5z$a s v d
d) $t^2+t$a s v d
e) $2d^2+4d$a s v d
f) $5a^2+5a$a s v d
g) $3b^2-12b$a s v d
h) $6h^2+9h$a s v d
i) $8k^2-20k$a s v d
j) $12j^3+24j^2$a s v d
k) $4e^4-2e^2$a s v d
l) $30y^5-55y^2$a s v d

## Question 7

Fully factorise the following expressions

a) $xy+x$a s v d
b) $2a+ab$a s v d
c) $7m+14n$a s v d
d) $8y-4xy$a s v d
e) $20e-5e^2$a s v d
f) $5r^2-6pr$a s v d
g) $5gh-5gi$a s v d
h) $10x^2+15x$a s v d
i) $12w^2-6vw$a s v d
j) $8a^2b+8ab^2$a s v d
k) $2m^2n^2+8m^2$a s v d
l) $24g^2h-42gh^2$a s v d

## Question 8

Fully factorise the following expressions

a) $2x+2y+2z$a s v d
b) $8x+4y+12z$a s v d
c) $ab+ac+ad$a s v d
d) $2gh-gk+3gm$a s v d
e) $e^2-2e+5e$a s v d
f) $6t^3+6tu-18tv$a s v d
g) $10pq+5pr-50p$a s v d
h) $3w+3x-3y+3z$a s v d
i) $ab+2ac-3ad+5ae$a s v d
j) $4m^2+8mn-12mp^2+8mq$a s v d
k) $40t^4+5t^2u^2-5t^2v+25t^2w^2$a s v d
l) $21a^5-35a^2b^2+28a^2c^5-35a^2d+105$a s v d

## Question 9

Fully factorise the following expressions

a) $20xy-12xyz^2$a s v d
b) $21d^7e^3f-77d^2e^4$a s v d
c) $y+5y^{\frac12}$a s v d
d) $2z^4-3yz^{\frac32}$a s v d
e) $20x^2y^{\frac12}-80x^{\frac12}y$a s v d
f) $51a^{\frac53}b^{\frac13}-85a^{\frac53}b^2+153a^4b^{\frac13}$a s v d