Lesson Notes By Weeks and Term v4 - SHS 1

Lesson Video

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Performance objectives

• Define and identify perfect squares.
• Understand and use the difference of two squares formula.
• Factor quadratic expressions.
• Apply these concepts to solve problems involving area.

Lesson summary

This lesson builds upon our previous knowledge of algebraic expressions and factorisation. We will explore two special types of expressions: perfect square trinomials and the difference of two squares. Understanding these patterns is not just an abstract skill; it is a powerful tool that simplifies complex calculations and helps us solve real-world problems more efficiently. In Ghana, these concepts can be applied in areas like land measurement for farming, design and construction, and even in quick mental calculations for business at the market. By mastering these techniques, you will develop a deeper understanding of algebraic structure and enhance your problem-solving abilities.

Lesson notes

This lesson focuses on two key "shortcuts" in algebra. Let's break them down one by one. Part A: Perfect Square Trinomials

A trinomial is an algebraic expression with three terms (e.g., `x² + 5x + 6`). A perfect square trinomial is a special trinomial that is the result of squaring a binomial (a two-term expression).

The Patterns to Recognise: (a + b)² = (a + b)(a + b) = a² + ab + ba + b² = a² + 2ab + b² (a – b)² = (a – b)(a – b) = a² – ab – ba + b² = a² – 2ab + b²

How to Spot a Perfect Square Trinomial:

Evaluation guide

• Recognise perfect squares and apply the idea to solve problems , including the difference
• of two squares of binomials .
• 
•  𝑐𝑐(𝑎𝑎+𝑏𝑏)+𝑑𝑑(𝑎𝑎+𝑏𝑏), add the outside terms and take one of the common terms to be the final