Study S2 Mathematics Maths Further Expansion and factorisation - Geniebook

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
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