# Further Expansion And Factorisation

In this chapter, we will be discussing the below-mentioned topics in detail:

• Further Expansion of Algebraic Expressions
• Factorisation of Algebraic Expressions

Let’s understand this with the help of some examples:

Question 1:

Simplify \begin{align*} 3 \;p^3 \;q \;\times\; 7 \;p^2 \;q^2 \end{align*}

Solution:

​ \begin{align*} 3 p^3 q \times 7 p^2 q^2 &= 3 \times p \times p \times p \times q \times 7\times p \times p \times q \times q\\ \\ &= 21 \;p^5 \;q^3 \end{align*} ​

Question 2:

Expand $-5x (\;x – 7y\;)$

Solution:

\begin{align*} -5x (x – 7y) &= (-5x) (x) + (-5x) (-7y) \\ &= -5x^2 + 35xy \end{align*}

Question 3:

Expand and simplify $(\;3x – 2\;) (\;4x – 5\;)$

Solution:

\begin{align*} (3x – 2) (4x – 5) &= (3x) (4x) + (-2) (4x) + (3x) (- 5) + (-2) (-5) \\ &= 12x^2 – 8x – 15x +10 \\ &= 12x^2 – 23x +10 \\ \end{align*}

Question 4:

Expand and simplify $-2 (\;x – y\;) (\;7x -2y\;)$

Solution:

\begin{align*} -2 (x – y) (7x -2y) &= -2 (7x^2 – 2xy – 7xy + 2y^2) \\ &= -2 (7x^2 – 9xy + 2y^2) \\ &= -14x^2 +18xy – 4y^2 \\ \end{align*}

Question 5:

Factorise $9a^2b - 15ab + 3ab^2$ completely.

Solution:

We can extract out a common factor of $3ab$.

\begin{align*} 9a^2b - 15ab + 3ab^2 = 3ab (\;3a - 5 + b\;) \end{align*}

Question 6:

Factorise $25x^2 - 2y - 10x + 5xy$ completely.

Solution:

For this question, we do Factorisation by Grouping.

We can group $25x^2$ and $-10x$ together,  $-2y$ and $+5xy$ together.

\begin{align*} 25x^2 - 10x - 2y + 5xy &= 5x (5x - 2) +y (-2 + 5x) \\ &= (5x - 2) (5x + y) \end{align*}

Continue Learning
Algebraic Fractions Direct & Inverse Proportion
Congruence And Similarity Factorising Quadratic Expressions
Further Expansion And Factorisation Quadratic Equations And Graphs
Simultaneous Equation
Primary
Secondary
Book a free product demo
Suitable for primary & secondary
Our Education Consultants will get in touch with you to offer your child a complimentary Strength Analysis.
Book a free product demo
Suitable for primary & secondary
our educational content
Start practising and learning.
No Error
No Error
*By submitting your phone number, we have
your permission to contact you regarding
Let’s get learning!
resources now.
Error
Oops! Something went wrong.
Let’s refresh the page!
Turn your child's weaknesses into strengths
Turn your child's weaknesses into strengths
Trusted by over 220,000 students.

Error
Oops! Something went wrong.
Let’s refresh the page!
Error
Oops! Something went wrong.
Let’s refresh the page!