# Algebra - Cubic Identities

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

## Question 1

Expand

a) $(x+y)^3$a s v d
b) $(x-y)^3$a s v d
c) $(x+y)(x^2-xy+y^2)$a s v d
d) $(x-y)(x^2+xy+y^2)$a s v d

## Question 2

Expand

a) $(x+1)^3$a s v d
b) $(x+2)^3$a s v d
c) $(x+5)^3$a s v d
d) $(7+x)^3$a s v d
e) $(2x+1)^3$a s v d
f) $(3x+2)^3$a s v d
g) $(6y+z)^3$a s v d
h) $(a^2+2b)^3$a s v d

## Question 3

Expand

a) $(x-1)^3$a s v d
b) $(x-2)^3$a s v d
c) $(2x-1)^3$a s v d
d) $(2a-b)^3$a s v d
e) $(4x-3y)^3$a s v d
f) $(x^2-5)^3$a s v d
g) $(x^2-x)^3$a s v d
h) $(2a^2-3b^3)^3$a s v d

## Question 4

Factorise

a) $x^3+y^3$a s v d
b) $x^3+1$a s v d
c) $a^3+8$a s v d
d) $m^3+125$a s v d
e) $8p^3+1$a s v d
f) $27z^3+64$a s v d

## Question 5

Factorise

a) $x^3-y^3$a s v d
b) $x^3-1$a s v d
c) $y^3-64$a s v d
d) $27g^3-1$a s v d
e) $125g^3-27$a s v d
f) $343a^3-8p^3$a s v d

## Question 6

Expand and simplify

a) $\left(x+y\right)^3+\left(x-y\right)^3$a s v d
b) $\left(x+y\right)^3-\left(x-y\right)^3$a s v d
c) $\left(x-y\right)^3-\left(x+y\right)^3$a s v d
d) $\left(2x^2-3y\right)^3+\left(2x^2+3y\right)^3$a s v d

## Question 7

Factorise fully

a) $2x^3+2y^3$a s v d
b) $x^4-xy^3$a s v d
c) $x^3+y^3+x+y$a s v d
d) $2a^3+6a^2b+6ab^2+2b^3$a s v d
e) $x^3-y^3+x^2-y^2$a s v d
f) $a^6+2a^3b^3+b^6$a s v d

## Question 8

Simplify

a) $\frac{x^3+y^3}{x+y}$a s v d
b) $\frac{5x^3-5y^3}{x-y}$a s v d
c) $\frac{x^3-y^3}{6x-6y}$a s v d
d) $\frac{125t^3-1}{25t^2-1}$a s v d
e) $\frac{8a^3+b^3}{6a^2+ab-b^2}$a s v d
f) $\frac{x^3-y^3}{x-y}\div\frac{x^3+y^3+2xy(x+y)}{x+y}$a s v d

## Question 9

Factorise fully

a) $x^6+1$a s v d
b) $x^6-1$a s v d
c) $x^{24}+y^{24}$a s v d
d) $x^8-x^2$a s v d

## Question 10

a) If $x$ and $y$ are real numbers such that $x+y=7$ and $x^3+y^3=91$, find the value of $xy$.a s v d

b) If $x$ and $y$ are real numbers such that $x-y=1$ and $x^3-y^3=61$, find the value of $xy$.a s v d

## Question 11

a) Evaluate $\sqrt{\sqrt[3]{1000}+\sqrt[3]{1000+150(15)+125}}$a s v d