Simplifying Algebra: – Collecting like terms to simplify expressions.

SIMPLIFYING ALGEBRA Collecting like terms to simplify expressions. Grade 7 Mathematics: Simplifying Algebra – Collecting Like Terms Subtopic Navigator Introduction Understanding Like Terms Simplifying with Addition Simplifying with Subtraction Combining Multiple Variables Applications and Mixed Problems Cumulative Exercises Conclusion Lesson Objectives Understand what like terms are in algebra. Learn how to simplify expressions by collecting like terms. Practice addition and subtraction of like terms. Apply simplification in real algebraic contexts. Lesson Introduction In algebra, we often work with expressions containing variables and numbers. To simplify these expressions, we combine terms that are alike. Like terms are terms that have the same variable(s) raised to the same power. For example, [latex]3x[/latex] and [latex]7x[/latex] are like terms, but [latex]3x[/latex] and [latex]3y[/latex] are not. Simplifying expressions by collecting like terms makes them easier to work with in further calculations. Understanding Like Terms Like terms have identical variable parts. Only the numerical coefficients can differ. Constants (numbers without variables) are also considered like terms with each other. Example 1: Identify the like terms in [latex]4x + 7 + 3x - 2[/latex]. Solution: [latex]4x[/latex] and [latex]3x[/latex] are like terms. [latex]7[/latex] and [latex]-2[/latex] are like terms (constants). Example 2: Which are like terms in [latex]2y, ; 5x, ; -3y, ; 8[/latex]? Solution: [latex]2y[/latex] and [latex]-3y[/latex] are like terms. [latex]5x[/latex] is different, and [latex]8[/latex] is a constant. Exercises (Understanding Like Terms) Circle the like terms: [latex]6a, ; 4b, ; -2a, ; 9[/latex] Which terms are like in [latex]3p, ; 5q, ; -7p, ; 2q[/latex]? Simplifying with Addition When simplifying by addition, add the coefficients of like terms while keeping the variable part unchanged. Example 3: Simplify [latex]5x + 3x[/latex]. Solution: [latex](5 + 3)x = 8x[/latex]. Example 4: Simplify [latex]7y + 2y + y[/latex]. Solution: [latex](7+2+1)y = 10y[/latex]. Exercises (Addition of Like Terms) Simplify [latex]4m + 9m[/latex]. Simplify [latex]6p + p + 2p[/latex]. Simplifying with Subtraction When simplifying by subtraction, subtract the coefficients of like terms while keeping the variable part unchanged. Example 5: Simplify [latex]10x - 6x[/latex]. Solution: [latex](10-6)x = 4x[/latex]. Example 6: Simplify [latex]8y - 3y + y[/latex]. Solution: [latex](8 - 3 + 1)y = 6y[/latex]. Exercises (Subtraction of Like Terms) Simplify [latex]12a - 4a[/latex]. Simplify [latex]5p - 2p + 3p[/latex]. Combining Multiple Variables When simplifying an expression with multiple variables, collect like terms separately for each variable. Example 7: Simplify [latex]3x + 2y + 5x - y[/latex]. Solution: Combine [latex]3x + 5x = 8x[/latex]. Combine [latex]2y - y = y[/latex]. Final answer: [latex]8x + y[/latex]. Example 8: Simplify [latex]4a + 3b - 2a + 5b[/latex]. Solution: [latex]4a - 2a = 2a[/latex], [latex]3b + 5b = 8b[/latex]. Final answer: [latex]2a + 8b[/latex]. Exercises (Multiple Variables) Simplify [latex]6x + 3y - 2x + y[/latex]. Simplify [latex]7m - 4n + 3m + 6n[/latex]. Applications and Mixed Problems Example 9: A rectangle has length [latex](5x + 2)[/latex] and width [latex](3x + 4)[/latex]. Write an expression for its perimeter. Solution: Perimeter = [latex]2(text{length} + text{width}) = 2((5x+2) + (3x+4))[/latex]. = [latex]2(8x + 6) = 16x + 12[/latex]. Example 10: The sum of three consecutive numbers is expressed as [latex](n + (n+1) + (n+2))[/latex]. Simplify. Solution: [latex]n + n + 1 + n + 2 = 3n + 3[/latex]. Exercises (Applications) The perimeter of a square is [latex]4(3x + 2)[/latex]. Simplify the expression. Simplify [latex](2y + 3) + (5y - 1)[/latex]. Cumulative Exercises Simplify [latex]7a + 2a - 3a[/latex]. Simplify [latex]5x + 4y + 3x - y[/latex]. Simplify [latex]6m - 2m + 9[/latex]. Simplify [latex]10p + 7q - 4p + 3q[/latex]. Simplify [latex]8x - 3x + 5x[/latex]. Simplify [latex]12y + 5 - 7y + 2[/latex]. Simplify [latex]3a + 4b - a + 2b[/latex]. Simplify [latex]15x - 9 + 5x + 3[/latex]. Simplify [latex]2p + 3q + 4p - q + 7[/latex]. Simplify [latex]6m + 2n - 3m + 4n - 5[/latex]. Conclusion/Recap In this lesson, we learned how to identify and combine like terms to simplify algebraic expressions. By carefully adding or subtracting the coefficients of like terms, we can reduce expressions to their simplest forms. This skill is foundational in algebra, making equations easier to solve and apply in problem-solving situations. Clip It! Share your ANSWER in the Chat. Indicate TITLE e.g Linear Equation 1. .....2. e.t.c