AlgèbreFacile

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📚 Essential Reference

Algebra Formulas

All essential formulas to succeed in algebra! Save these notes and consult them anytime.

Notable Identities

Factorizations

Advanced Formulas

🍕Fraction Rules

Numérateur / Dénominateur

Numerator (top) over denominator (bottom)

1a se simplifie en a

Special fraction

11 se simplifie en 1

Unit fraction

0a se simplifie en 0

Zero numerator

a0 est indéfini

Division by zero undefined

-ab = a/-b

Equivalent negative fractions

-ab se simplifie en -ab

Negative sign simplification

-ab ≠ ab

Watch the signs!

➕Addition and Subtraction

ab + cb = (a+c)b

Same denominator: add numerators

a + bc = (ac + b)c

Whole number + fraction

ab + cd = (ad + bc)bd

Different denominators

ab - cb = (a-c)b

Subtraction same denominator

a - bc = (ac - b)c

Whole number - fraction

ab - cd = (ad - bc)bd

Subtraction different denominators

✖️Multiplication

ab × cd = (ac)(bd)

Multiply numerators and denominators

a × bc = (a×b)c = abc

Whole number × fraction

ab × c = (a×c)b = acb

Fraction × whole number

➗Division

(ab) ÷ (cd) = (ab) × (dc) = adbc

Division = multiply by reciprocal

(ac) ÷ (bc) = (ac) × (cb) = ab

Simplification after division

(ab) ÷ c = a(b×c) = abc

Fraction ÷ whole number

🔄Cancellation Rules

aa se simplifie en 1

Same numerator and denominator

abac se simplifie en bc

Common factor 'a' cancels

a·bc se simplifie en abc

No cancellation possible

a·cbc se simplifie en ab

Factor 'c' cancels

a·ba se simplifie en b

Factor 'a' cancels completely

aa·b se simplifie en 1b

Factor 'a' cancels at numerator

⚠️Be Careful - Common Mistakes

ab + cd ≠ (a+c)(b+d)

❌ Don't add directly

2+12 = 52 (et NON 32)

Convert whole number properly

🔢Order of Operations

Parentheses: (10 - 2) × 4 = 8 × 4 = 32

Always calculate what's in parentheses first

Exponents: 3² + 4 = 9 + 4 = 13

Powers before multiplication/division/addition/subtraction

Multiplication and Division: 8 ÷ 2 × 3 = 4 × 3 = 12

Left to right if same priority

Addition and Subtraction: 10 - 3 + 2 = 7 + 2 = 9

Left to right, always last

💡Memory Aid PEMDAS

P - Parentheses ( )

Calculate what's in parentheses first

E - Exponents (powers)

Then exponents like 2³ or x²

M - Multiplication ×

Then multiplication

D - Division ÷

And division (left to right with M)

A - Addition +

Then addition

S - Subtraction −

Finally subtraction (left to right with A)

⬛Notable Identities - Squares

(a + b)² = a² + 2ab + b²

Square of a sum

(a - b)² = a² - 2ab + b²

Square of a difference

a² + b² = (a + b)² - 2ab

Sum of squares (formula 1)

a² + b² = (a - b)² + 2ab

Sum of squares (formula 2)

🎲Notable Identities - Cubes

(a + b)³ = a³ + b³ + 3ab(a + b)

Cube of a sum

(a - b)³ = a³ - b³ - 3ab(a - b)

Cube of a difference

a³ + b³ = (a + b)³ - 3ab(a + b)

Sum of cubes (formula 1)

a³ - b³ = (a - b)³ + 3ab(a - b)

Difference of cubes (formula 1)

🔧Factorizations

a² - b² = (a + b)(a - b)

Difference of squares

a³ - b³ = (a - b)(a² + ab + b²)

Difference of cubes (factorization)

a³ + b³ = (a + b)(a² - ab + b²)

Sum of cubes (factorization)

🚀Advanced Formulas

a⁴ - b⁴ = (a² - b²)(a² + b²) = (a + b)(a - b)(a² + b²)

Difference of 4th powers

a⁴ + b⁴ = (a² + b²)² - 2a²b²

Sum of 4th powers (formula 1)

a⁴ + b⁴ = (a² + √(2ab) + b²)(a² - √(2ab) + b²)

Sum of 4th powers (factorization)

💡 Usage Tips

✅Memorize these formulas gradually - start with squares, then cubes
✅Practice with exercises to properly learn each formula
✅Use the copy button to save your favorite formulas
✅Come back regularly to review these formulas before exams