Page 1: Wzory Skróconego Mnożenia - Zadania z Rozwiązaniami
This page presents a series of wzory skróconego mnożenia zadania with detailed solutions, focusing on squaring binomials and using the difference of squares formula. The problems involve complex expressions with square roots and algebraic terms.
Example: (√2 + 4)² = (√2)² + 2•√2•4 + 4² = 2 + 8√2 + 16 = 18 + 8√2
This example demonstrates the application of the square of a sum formula (a + b)² = a² + 2ab + b². The solution is broken down step-by-step, showing how to handle square roots in the process.
Example: (3√6 - √2)² = (3√6)² - 2•3√6•√2 + (√2)² = 54 - 6√12 + 2 = 56 - 12√3
This problem illustrates the use of the square of a difference formula (a - b)² = a² - 2ab + b². The solution involves simplifying complex square root expressions.
Example: (2√6 - 3√3)² = 24 - 2•2√6•3√3 + 27 = 51 - 12√18 = 51 - 36√2
Another application of the square of a difference formula, this example shows how to simplify expressions with multiple square roots.
Example: (3√10 + 2√2)² = 90 + 2•3√10•2√2 + 8 = 98 + 12√20 = 98 + 24√5
This problem demonstrates the square of a sum formula with more complex square root terms.
Example: (√3 - √6)(√3 + √6) = (√3)² - (√6)² = 3 - 6 = -3
This example showcases the difference of squares formula (a² - b² = (a + b)(a - b)) applied to square root expressions.
Example: (3√2 - √7)(3√2 + √7) = (3√2)² - (√7)² = 18 - 7 = 11
Another application of the difference of squares formula, this time with more complex terms.
Highlight: These wzory skróconego mnożenia przykłady provide excellent practice for students preparing for exams or seeking to master algebraic manipulation techniques.
The page serves as a valuable resource for students studying wzory skróconego mnożenia kwadrat and related concepts, offering a range of problems that could appear in wzory skróconego mnożenia zadania maturalne PDF or wzory skróconego mnożenia zadania 1 liceum materials.
