Questions and Answers
What are perfect square trinomials?
The square of a binomial.
The Perfect Square Formula is: (a+b)^2 = ____ + 2ab + ____.
a^2, b^2
What is the result of (2x - 4y^2)^2?
4x^2 - 16xy^2 + 16y^4
What is the result of multiplying (2x + 3)(2x + 3)?
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What is the difference of two perfect squares formula?
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What is the result of multiplying (x - 4)(x + 4)?
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Study Notes
Perfect Square Trinomials
- Represents the square of a binomial expression.
Perfect Square Formula
- Formula: ((a+b)^2 = a^2 + 2ab + b^2)
Example 1
- Squaring the binomial ((2x - 4y^2)) results in:
- ((2x - 4y^2)^2 = 4x^2 - 16xy^2 + 16y^4)
Example 2
- Multiplying ((2x + 3)(2x + 3)) using the perfect square formula:
- Identify it as ((a + b)(a + b)) with (a = 2x) and (b = 3).
- Calculation yields:
- ((2x)^2 + 2(2x)(3) + (3)^2 = 4x^2 + 12x + 9)
Difference of Two Perfect Squares
- Involves the multiplication of a binomial sum and the difference of the same terms.
- Formula: ((a + b)(a - b) = a^2 - b^2)
Example 3
- Multiplying ((x - 4)(x + 4)) demonstrates the difference of two squares:
- Calculation leads to:
- ((x + 4)(x - 4) = x^2 - 4^2 = x^2 - 16)
- Calculation leads to:
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Description
This set of flashcards covers key concepts about perfect square trinomials and the perfect square formula. Learn how to apply these definitions and examples to solve problems involving the square of a binomial effectively.
