Algebra

Algebraic Expressions, Identities and Linear Equations

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Overview

Algebra forms the bridge between arithmetic and higher mathematics, making it a crucial topic for MAHA TET Paper II. This section tests your ability to manipulate symbols, simplify expressions, apply standard identities and solve equations — skills essential for teaching upper-primary students who encounter formal algebra for the first time in Classes VI–VIII.

Expect questions that assess both content knowledge and pedagogical understanding. You must know how to form and simplify algebraic expressions, recall and apply the four standard identities, and solve linear equations in one or two variables. Questions often combine these skills — for instance, using an identity to simplify an expression before solving an equation.

Mastering this topic also strengthens your preparation for geometry (where algebraic methods appear in mensuration formulas) and data handling (where expressions describe relationships). Allocate sufficient practice time here; the concepts reappear across the mathematics curriculum.

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Key Concepts

• **Algebraic Expression**: A combination of constants, variables and operations (e.g., 3x + 5, 2a² − 7ab + 4). It does not contain an equality sign.

• **Terms, Coefficients and Like Terms**: Each part separated by + or − is a term. The numerical factor is the coefficient. Like terms share the same variable part (e.g., 5xy and −2xy are like terms).

• **Monomial, Binomial, Trinomial, Polynomial**: Classified by number of terms — one term (monomial), two terms (binomial), three terms (trinomial), many terms (polynomial).

• **Degree of an Expression**: The highest sum of exponents of variables in any term. For 4x³y², the degree is 3 + 2 = 5.

• **Algebraic Identity**: An equation true for all values of the variables. Differs from an equation, which is true only for specific values.

• **Linear Equation**: An equation where the highest power of the variable is 1. Standard form in one variable: ax + b = 0 (a ≠ 0).

• **Solution / Root**: The value of the variable that satisfies the equation.

• **Transposition Rule**: When a term moves across the equality sign, its sign changes (equivalent to adding/subtracting on both sides).

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Formulas / Key Facts

### Standard Algebraic Identities

| Identity | Expanded Form | |----------|---------------| | (a + b)² | a² + 2ab + b² | | (a − b)² | a² − 2ab + b² | | (a + b)(a − b) | a² − b² | | (x + a)(x + b) | x² + (a + b)x + ab |