Ai made ppt on Algebra

1. Algebraic Expressions
By Shivangi Tiwari

2. Introduction to Algebraic Expressions
 An algebraic expression is a mathematical phrase combining numbers, variables
(letters representing unknowns), and operation symbols (+, −, ×, ÷).
 They help describe general arithmetic relationships and unknown quantities in
math.
 Examples:
 3x+23x+2,
 a2−ba2−b,
 4xy4xy
 Expansion Question:
How are algebraic expressions different from arithmetic expressions?

3. Components of Algebraic Expressions
 Constants: Fixed numbers (e.g., 7, −3, 1/2).
 Variables: Symbols representing unknown or changing values (e.g., x,y,ax,y,a).
 Coefficients: Numbers multiplying variables (e.g., 5 in 5x5x).
 Operators: Symbols representing the operation (e.g., +, −, ×, ÷).
 Elaboration:
Understanding these parts helps in simplifying and evaluating expressions correctly.
 Expansion Question:
Given the expression 6ab−4b+c6ab−4b+c, identify the constants, variables, and
coefficients.

4. Forms of Algebraic Expressions
 Monomial: One term
(e.g., 7x7x, −3a−3a, 8)
 Binomial: Two terms
(e.g., x+5x+5, 3y−43y−4)
 Trinomial: Three terms
(e.g., 2x2+3x+12x2+3x+1)
 Polynomial: One or more terms (general
term including above)
 Elaboration:
Terms are separated by plus or minus
signs.
 Expansion Question:
Classify each as monomial,
binomial, trinomial, or
polynomial:
a) 4x34x3,
b) y+2zy+2z,
c) a2+b2+c2a2+b2+c2,
d) 5x2−3x+7−15x2−3x+7−1

5. Examples of Algebraic Expressions
 3x+2y−7: 3 terms, variables xx, yy, constants and coefficients
 4x−104x−10: binomial with variable xx
 2x2−3xy+52x2−3xy+5: trinomial with degree 2
 x+yx+y: binomial
 5a+3b+c5a+3b+c: trinomial with three variables
 Elaboration:
Identify variables, coefficients, and constants in each.
 Expansion Question:
Write your own trinomial and explain each component.

6. Operations on Algebraic Expressions
Addition and Subtraction
Combine like terms (same variables and same powers):
(3x+2y)+(4x−y)=7x+y(3x+2y)+(4x−y)=7x+y
(5a−3b)−(2a+b)=3a−4b(5a−3b)−(2a+b)=3a−4b

7. Operations on Algebraic Expressions
Multiplication
Distributive Property:
2(x+5)=2x+102(x+5)=2x+10
Multiply monomials:
X*X=X^2

8. Operations on Algebraic Expressions
Division
Divide coefficients and subtract exponents:
X2/X=x

9. Multiplying Double and Triple Brackets
Double Brackets (Binomials) — FOIL Method
(x+a)(x+b)=x2+(a+b)x+ab(x+a)(x+b)=x2+(a+b)x+ab
Example:
(x+2)(x+3)=x2+3x+2x+6=x2+5x+6(x+2)
(x+3)=x2+3x+2x+6=x2+5x+6

10. Triple Brackets
Multiply two brackets first, then multiply the result with
the third.
(x+1)(x−2)(x+3)(x+1)(x−2)(x+3)Step 1:
(x+1)(x−2)=x2−x−2(x+1)(x−2)=x2−x−2Step 2:
(x2−x−2)(x+3)=x3+2x2−5x−6(x2−x−2)
(x+3)=x3+2x2−5x−6

11. Practice Problems
 Q1: Simplify 5x+3y−2x+45x+3y−2x+4
 Q2: Evaluate 4x2−3x+74x2−3x+7 when x=2x=2
 Q3: Identify the coefficient of yy in 8y−3x+68y−3x+6
 Q4: Represent the sum of three consecutive integers as an algebraic
expression
 Q5: Write and simplify an expression for the perimeter of a rectangle with
length ll and width ww

12. Practice Problems
 Q6: Expand and simplify (x+4)(x−5)(x+4)(x−5)
 Q7: Expand and simplify (2x+3)(x−1)(2x+3)(x−1)
 Q8: Expand and simplify (x+2)(x+3)(x−4)(x+2)(x+3)(x−4)
 Q9: Expand and simplify (3x−1)(x+2)(x−3)(3x−1)(x+2)(x−3)
 Q10: If A=(x+2)(x−3)A=(x+2)(x−3) and B=(x−1)B=(x−1), find and
simplify A×BA×B

13. : Common Mistakes and Key Takeaways
Common Mistakes:
 Combining unlike terms incorrectly
 Incorrect use of distributive property
 Ignoring exponent rules when multiplying/dividing powers
Key Takeaways:
 Algebraic expressions generalize arithmetic by using variables.
 Understanding components and operations is essential for simplifying and solving
problems.
 Mastery of algebraic expressions is foundational for higher math topics.

14. End of Presentation
Thank You.
Presented by Shivangi Tiwari