# Algebra - Expanding Double Brackets

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## Question 1

Expand the brackets

a) $(x+1)(x+2)$a s v d
b) $(x+2)(x+3)$a s v d
c) $(x+4)(x+6)$a s v d
d) $(x+7)(x+2)$a s v d
e) $(x+2)(x+10)$a s v d
f) $(x+9)(x+3)$a s v d
g) $(x+4)(x+7)$a s v d
h) $(x+10)(x+11)$a s v d
i) $(x+1)(x+50)$a s v d
j) $(x+4)(x+4)$a s v d
k) ${(x+4)}^2$a s v d
l) ${(x+5)}^2$a s v d

## Question 2

Expand the brackets

a) $(x-1)(x-2)$a s v d
b) $(x-3)(x-5)$a s v d
c) $(x-6)(x-7)$a s v d
d) $(x-7)(x-3)$a s v d
e) $(x-9)(x-8)$a s v d
f) $(x-3)(x-10)$a s v d
g) $(x-1)(x-18)$a s v d
h) $(x-13)(x-12)$a s v d
i) $(x-3)(x-3)$a s v d
j) ${(x-3)}^2$a s v d
k) ${(x-6)}^2$a s v d
l) ${(x-10)}^2$a s v d

## Question 3

Expand the brackets

a) $(x+5)(x-2)$a s v d
b) $(x+6)(x-2)$a s v d
c) $(x+2)(x-5)$a s v d
d) $(x+5)(x-7)$a s v d
e) $(x-5)(x+2)$a s v d
f) $(x-10)(x+3)$a s v d
g) $(x-3)(x+6)$a s v d
h) $(x-9)(x+10)$a s v d
i) $(x-15)(x+22)$a s v d
j) $(x-9)(x+9)$a s v d
k) $(x-4)(x+4)$a s v d
l) $(x-10)(x+10)$a s v d

## Question 4

Expand the brackets

a) $(2x+1)(x+2)$a s v d
b) $(3x+2)(x+1)$a s v d
c) $(5x+3)(x+4)$a s v d
d) $(10x+1)(x+1)$a s v d
e) $(6x+5)(x+4)$a s v d
f) $(8x+3)(x+7)$a s v d
g) $(9x+1)(x+10)$a s v d
h) $(2x-1)(x+3)$a s v d
i) $(3x-4)(x+4)$a s v d
j) $(2x+3)(x-1)$a s v d
k) $(4x+3)(x-2)$a s v d
l) $(2x-2)(x-1)$a s v d
m) $(3x-4)(x-3)$a s v d
n) $(x+3)(2x+1)$a s v d
o) $(x-3)(3x+2)$a s v d
p) $(x-4)(4x-5)$a s v d

## Question 5

Expand the brackets

a) $(2x+1)(3x+1)$a s v d
b) $(2x+2)(3x+4)$a s v d
c) $(3x+4)(5x+2)$a s v d
d) $(6x+1)(8x+5)$a s v d
e) $(7x+2)(10x+1)$a s v d
f) $(3x+5)(12x+3)$a s v d
g) $(2x-1)(3x+2)$a s v d
h) $(3x+1)(4x-2)$a s v d
i) $(5x-6)(2x+2)$a s v d
j) $(3x-2)(2x-3)$a s v d
k) $(5x-1)(3x-5)$a s v d
l) $(8x-2)(6x-3)$a s v d

## Question 6

Expand the brackets

a) $(3+x)(x-2)$a s v d
b) $(4-x)(x-4)$a s v d
c) $(2x-3)(3+x)$a s v d
d) $(4-x)(5-2x)$a s v d
e) $(y-2)(4-2y)$a s v d
f) $(4-z)(4+z)$a s v d
g) ${(2x+3)}^2$a s v d
h) ${(4x-3)}^2$a s v d
i) ${(8-r)}^2$a s v d
j) ${(3-2e)}^2$a s v d
k) $(a+1)(b+2)$a s v d
l) $(2m-3)(n+2)$a s v d
m) $(4-5p)(3-2p)$a s v d
n) $(x^2+3)(x^2+4)$a s v d
o) $(3x^2+2)(2x^2+1)$a s v d
p) $(5x^2-7)(2x^2+3)$a s v d
q) $(8+k^2)(k^2-4)$a s v d
r) $(q+7)(q^2+2)$a s v d
s) $(p^3-1)(p^4+2)$a s v d
t) $(9f^2+8)(3f-2)$a s v d

## Question 7

Expand the brackets

a) $\left(\frac1x+x\right)(x+2)$a s v d
b) $\left(\frac{1}{x}+1\right)\left(\frac{1}{x}+1\right)$a s v d
c) $\left(\frac{1}{x}+x\right)\left(\frac{1}{x}+x\right)$a s v d
d) $\left(\frac{2}{x}+x\right)\left(\frac{3}{x}+x\right)$a s v d
e) $\left(\frac{1}{x^2}+x\right)\left(\frac{1}{x^2}+x\right)$a s v d
f) $\left(\frac{1}{x^2}+x^2\right)^2$a s v d
g) $\left(\frac{1}{x^2}+\frac{1}{x}\right)^2$a s v d
h) $\left(\frac{2}{x^2}+x^2\right)^2$a s v d
i) $\left(\frac{2}{x^2}+\frac{3}{x}\right)^2$a s v d
j) $\left(4x+\frac{1}{4x}\right)^2$a s v d
k) $\left(x-\frac{1}{x}\right)^2$a s v d
l) $\left(2x-\frac{1}{x^2}\right)\left(x+\frac{3}{x^2}\right)$a s v d

## Question 8

Expand the brackets and simplify

a) $(x+2)(x+3)+4$a s v d
b) $(x+5)(x+2)+10$a s v d
c) $(x+2)(x-2)+4$a s v d
d) ${(x+6)}^2+12x$a s v d
e) $(2x+3)(x+1)+x^2$a s v d
f) $(x-3)(3x+2)-x^2$a s v d
g) $(5x-2)(6x+1)+2x+1$a s v d
h) $(x+4)(x+5)+2(x+3)$a s v d
i) $(2x+1)(x+1)+3(x-2)$a s v d
j) $(5x-3)(2x-1)-(x+2)$a s v d
k) ${(3x-1)}^2+5(x-3)$a s v d
l) ${(2-3x)}^2+x(x+1)$a s v d
m) $(4x-3)(6x+8)+x(2x-3)$a s v d
n) $(3x^2+1)(2x^2-3)+3x^2(x-4)$a s v d

## Question 9

Expand the brackets and simplify

a) $(x+1)(x+2)+(x+2)(x+3)$a s v d
b) $(x+5)(x+7)+(x+3)(x+8)$a s v d
c) $(x+3)(x-2)+(x+5)(x-2)$a s v d
d) $(2x-1)(x+2)+(3x+2)(x-2)$a s v d
e) $(6x+3)(x-1)+(4x-1)(5x+6)$a s v d
f) $(3x+1)(3x+4)-(2x+2)(x+1)$a s v d
g) $(3x-1)(2x-3)-(4x-1)(3x-2)$a s v d
h) ${(5x-2)}^2+(2x-1)(5x-2)$a s v d
i) ${(2x+1)}^2+{(x+9)}^2$a s v d
j) ${(4x-1)}^2-{(3x+2)}^2$a s v d
k) $(2x-5)(2x+5)-(4x-1)(4x+1)$a s v d
l) $(2x+2)(x-6)-{(x-1)}^2+(x+6)(2x-3)$a s v d

## Question 10

Expand the brackets and simplify

a) $(x+y+1)(x+y+1)$a s v d
b) $(x^2+x+1)(x^2+x+1)$a s v d
c) ${(3y+2z+2)}^2$a s v d
d) $(3a+2b+c)(4a+3b+2c)$a s v d
e) $(p-q+r)(q-p-r)$a s v d
f) ${(x+1)}^3$a s v d
g) ${(2y-1)}^3$a s v d
h) ${(4z-3)}^2{(2w+5)}^2$a s v d
i) $s^2(3s-5t+8u)(5s-5t-u)$a s v d
j) $3{(x+y)}^2(4x-7y+z)(2x^2-5y-8)$a s v d
k) ${(5-s)}^3-{(4s+1)}^3$a s v d
l) $3{(2p-1)}^2{(7q+3)}^2-8{(7-8q)}^2\times 3{(11q+9)}^2$a s v d