Perfect Square Trinomials
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Slide 1 - Perfect Square Trinomials
- 2.3 – pp. 45-46
Slide 2 - Recognizing:
- (a + b)2 = a2 + 2ab + b2
- (a + b)2 = a2 – 2ab + b2
- These trinomials are both squares because they are each the product of two (2) equal factors. Trinomials like these (squares) will have these characteristics:
- 1. Two (2) terms, such as a2 and b2, must be squares.
- 2. The absolute value of the other term must be equal to twice the product of the square roots of the terms that are squares.
Slide 3 - Factoring a Perfect Square Trinomial:
- If the trinomial is not already in the form a2 + 2ab + b2, with the squared terms on the ends and product of the terms in the middle, then rewrite it in this form.
- Then write down the square roots of the first and last terms.
- Then write between them the sign of the trinomial’s middle term.
- Write the binomial to be squared.
- NOTE: When factoring trinomials, usually only the positive (+) square root is taken.
Slide 4 - Example:
- M2 – 8m + 16