Fully Factorise

Fully factorising algebraic expressions is a fundamental skill in mathematics that helps simplify complex equations and solve problems efficiently. For example, consider the expression 3(x-2)^2 - (x-2). To fully factorise this, you start by recognizing the common factor (x-2) in both terms. First, rewrite the expression by factoring out (x-2): 3(x-2)^2 - (x-2) = (x-2)(3(x-2) - 1). Next, simplify the expression inside the parentheses: 3(x-2) - 1 = 3x - 6 - 1 = 3x - 7. Therefore, the fully factorised form is (x-2)(3x - 7). Understanding how to spot common factors and applying the distributive property are key to mastering factorisation. This process is widely applicable in algebra to solve equations, simplify expressions, and analyze functions. Moreover, practicing such factorisation enhances problem-solving skills and prepares students for exams and real-world math applications. For students and teachers, using step-by-step methods to break down expressions improves comprehension and retention. In particular, focus on recognizing patterns like difference of squares, perfect square trinomials, and factoring by grouping to expand your toolkit. By incorporating these strategies in your math study routine, you can approach complex questions with confidence and precision, making learning math an engaging and rewarding experience.