Lesson 1.10: Algebra

Introduction:
Algebra is a vital part of SSC quantitative aptitude. Questions often involve solving equations, simplifying expressions, and using formulas efficiently.

1. Basics of Algebra

• Variable: Symbol (like x, y) representing unknown quantity.

• Constants: Fixed numbers.

• Expressions: Combination of variables and constants using +, −, ×, ÷.
  Example: $3x+5$, $2y-7$

• Equation: Statement that two expressions are equal.
  Example: $2x+5=15$

2. Solving Linear Equations

• Method:

$$2x+5=15⟹2x=15-5⟹2x=10⟹x=5$$

• Tips for SSC Exams:

  • Solve step by step.

  • Check for negative values or fractions.

  • Use shortcut formulas for simultaneous equations if allowed.

3. Algebraic Identities

• Important Identities:

1. (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2

2. (a−b)2=a2−2ab+b2(a-b)^2 = a^2 – 2ab + b^2(a−b)2=a2−2ab+b2

3. a2−b2=(a−b)(a+b)a^2 – b^2 = (a-b)(a+b)a2−b2=(a−b)(a+b)

4. (x+y+z)2=x2+y2+z2+2(xy+yz+zx)(x+y+z)^2 = x^2 + y^2 + z^2 + 2(xy+yz+zx)(x+y+z)2=x2+y2+z2+2(xy+yz+zx)

• Usage: Simplifies complicated expressions in SSC exam questions.

4. Factorization

• Method: Express as product of simpler expressions.
  Example: x2−9=(x−3)(x+3)x^2 – 9 = (x-3)(x+3)x2−9=(x−3)(x+3)

• Tips: Recognize patterns using identities.

5. SSC Exam Tips

• Memorize basic formulas for speed.

• Check calculations for simple mistakes.

• Practice simplifying expressions and solving linear equations quickly.

• Word problems often convert to linear equations.

6. Practice Questions

1. Solve: $3x+7=19$

2. Factorize: x2−16x^2 – 16x2−16

3. Solve: $2x-3=7$

4. Simplify: (x+5)2−(x−5)2(x+5)^2 – (x-5)^2(x+5)2−(x−5)2

5. Solve simultaneous equations:
   $x+y=10$
   $x-y=4$