Hi everyone! This chapter is all about Factorisation<\/span>. It’s like the opposite of expanding algebraic expressions. Instead of multiplying things out, we break them down into simpler parts (factors).<\/p>\n Factorisation is the process of writing an algebraic expression as a product of two or more expressions. Think of it like finding the prime factors of a number, but with algebraic expressions.<\/p>\n Example: x\u00b2 + 5x + 6 can be factored as (x + 2)(x + 3).<\/p>\n<\/p><\/div>\n Here are some common methods:<\/p>\n Look for terms that have a common factor (number or variable) and factor it out.<\/p>\n Example: 2x + 4 = 2(x + 2) (2 is the common factor).<\/p>\n Example: xy + xz = x(y + z) (x is the common factor).<\/p>\n<\/p><\/div>\n Sometimes, you can group terms together to find common factors.<\/p>\n Example: xy + 2x + 3y + 6 = x(y + 2) + 3(y + 2) = (x + 3)(y + 2).<\/p>\n<\/p><\/div>\n Recognize expressions that fit known identities (like a\u00b2 – b\u00b2 = (a + b)(a – b), or a\u00b2 + 2ab + b\u00b2 = (a + b)\u00b2) and use them to factor.<\/p>\n Example: x\u00b2 – 9 = (x + 3)(x – 3) (using the identity a\u00b2 – b\u00b2 = (a + b)(a – b)).<\/p>\n Example: x\u00b2 + 6x + 9 = (x + 3)\u00b2 (using the identity a\u00b2 + 2ab + b\u00b2 = (a + b)\u00b2).<\/p>\n<\/p><\/div>\n For expressions like ax\u00b2 + bx + c, find two numbers whose sum is ‘b’ and product is ‘ac’. Then split the middle term and factor by grouping.<\/p>\n Example: x\u00b2 + 5x + 6. We need two numbers whose sum is 5 and product is 6. The numbers are 2 and 3.<\/p>\n x\u00b2 + 5x + 6 = x\u00b2 + 2x + 3x + 6 = x(x + 2) + 3(x + 2) = (x + 3)(x + 2).<\/p>\n<\/p><\/div>\n Factorisation can make complex expressions easier to work with.<\/p>\n<\/p><\/div>\n Factorisation is often used to solve quadratic equations and other polynomial equations.<\/p>\n<\/p><\/div>\n In geometry, factorisation can help find dimensions when the area or volume is given as an algebraic expression.<\/p>\n<\/p><\/div>\n Many word problems in algebra can be solved more easily using factorisation.<\/p>\n<\/p><\/div>\n Factorisation is a very important skill in algebra, so make sure you practice lots of examples!<\/p>\n 1. **Area of a Rectangle:** The area of a rectangular garden is given by the expression x\u00b2 + 7x + 10. If the length of the garden is (x + 5), what is the width?<\/p>\n 2. **Volume of a Cuboid:** The volume of a cuboid is given by the expression x\u00b3 + 6x\u00b2 + 11x + 6. If the length is (x + 1) and the width is (x + 2), what is the height?<\/p>\n 3. **Cost of Tiles:** A bathroom floor requires tiles. The total cost of the tiles is given by the expression 4x\u00b2 + 12x + 9, where ‘x’ is related to the tile size. Factor the expression to determine possible dimensions related to the tiles.<\/p>\n 4. **Simplifying a Rational Expression:** Simplify the expression: (x\u00b2 – 4) \/ (x\u00b2 + 4x + 4)<\/p>\n 5. **Surface Area of a Cube:** The surface area of a cube is given by the expression 6x\u00b2 + 24x + 24. What is the side length of the cube?<\/p>\n 6. **Factoring a Cubic Expression:** Factor completely: x\u00b3 – 8<\/p>\n 7. **Factoring a Trinomial:** Factor completely: 2x\u00b2 + 5x – 3<\/p>\n 8. **Area of a Triangle:** The area of a triangle is given by the expression (x\u00b3 + 5x\u00b2 + 6x)\/2. If the base of the triangle is (x + 2), what is the height?<\/p>\n 9. **Simplifying a Complex Fraction:** Simplify: [(x\u00b2 + 2x – 3)\/(x + 3)] \/ [(x\u00b2 – 1)\/(x + 1)]<\/p>\n 10. **Factoring by Grouping:** Factor completely: xy + 5x – 2y – 10<\/p>\n <\/body> Factorisation – Class 8 Hi everyone! This chapter is all about Factorisation. It’s like the opposite of expanding algebraic expressions. Instead of multiplying things out, we break them down into simpler parts (factors). What is Factorisation? Factorisation is the process…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-162686","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"\nWhat is Factorisation?<\/h2>\n
Methods of Factorisation<\/h2>\n
1. Common Factors:<\/h3>\n
2. Grouping Terms:<\/h3>\n
3. Using Identities:<\/h3>\n
4. Middle Term Splitting (for quadratic expressions):<\/h3>\n
Applications of Factorisation<\/h2>\n
1. Simplifying Algebraic Expressions:<\/h3>\n
2. Solving Equations:<\/h3>\n
3. Finding Areas and Volumes:<\/h3>\n
4. Problem Solving:<\/h3>\n
Factorisation Quiz – Tough Application Problems<\/h1>\n
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