Course Content
Algebra 1
0/14
Algebra 2
0/16
Trigonometry 1
0/16
Coordinate Geometry of the Line
0/14
Probability 1
0/13
Geometry 1
0/6
Differential Calculus
0/16
Trigonometry 2
0/10
Sequences & Series
0/12
Statistics 1
0/12
Coordinate Geometry of the Circle
0/14
Algebra 3
0/14
Complex Numbers
0/12
Geometry 2
0/4
Integration
0/8
Differential Calculus Applications
0/8
Financial Maths
0/8
Length, Area & Volume
0/6
Probability 2
0/10
Functions
0/22
Statistics 2
0/6
Inferential Statistics
0/6
Digital Lessons

# Exercise Set D

## Question 1

Expand the following:

\begin{align}(x+2)^5\end{align}

$$x^5+10x^4+40x^3+80x^2+80x+32$$

Solution

\begin{align}(x+2)^5 &= \binom{5}{0}x^5(2^0) +\binom{5}{1}x^4(2^1)+\binom{5}{2}x^3(2^2)+\binom{5}{3}x^2(2^3)+\binom{5}{4}x^1(2^4)+\binom{5}{5}x^0(2^5)\\&=(1)x^5(1)+(5)x^4(2)+(10)x^3(4)+(10)x^2(8)+(5)x(16)+(1)(1)(32)\\&=x^5+10x^4+40x^3+80x^2+80x+32 \end{align}

Video Walkthrough

## Question 2

Expand the following:

\begin{align}(x+y)^3\end{align}

$$x^3+3x^2y+3xy^2+y^3$$

Solution

\begin{align}(x+y)^3 &= \binom{3}{0}x^3(y^0) +\binom{3}{1}x^2(y^1)+\binom{3}{2}x^1(y^2)+\binom{3}{3}x^0(y^3)\\&=(1)x^3(1)+(3)x^2(y)+(3)x(y^2)+(1)(1)(y^3)\\&=x^3+3x^2y+3xy^2+y^3 \end{align}

Video Walkthrough

## Question 3

Expand the following:

\begin{align}(x-6)^4\end{align}

$$x^4-24x^3+216x^2-864x+1296$$

Solution

\begin{align}(x-6)^4 &= \binom{4}{0}x^4(-6)^0 +\binom{4}{1}x^3(-6)^1+\binom{4}{2}x^2(-6)^2+\binom{4}{3}x^1(-6)^3+\binom{4}{4}x^0(-6)^4\\&=(1)x^4(1)+(4)x^3(-6)+(6)x^2(36)+(4)x(-216)+(1)(1)(1296)\\&=x^4-24x^3+216x^2-864x+1296 \end{align}

Video Walkthrough

## Question 4

Expand the following:

\begin{align}(2x+5)^3\end{align}

$$8x^3+60x^2+150x+125$$

Solution

\begin{align}(2x+5)^3 &= \binom{3}{0}(2x)^3(5^0) +\binom{3}{1}(2x)^2(5^1)+\binom{3}{2}(2x)^1(5^2)+\binom{3}{3}(2x)^0(5^3)\\&=(1)(8x^3)(1)+(3)(4x^2)(5)+(3)(2x)(25)+(1)(1)(125)\\&=8x^3+60x^2+150x+125 \end{align}

Video Walkthrough

## Question 5

Expand the following:

\begin{align}(2x-3y)^4\end{align}

$$16x^4-96x^3y+216x^2y^2-216xy^3+81y^4$$