Challenge 11 multiplying differences of squares
- 1. CHALLENGE 11 DIFFERENCES OF SQUARES 1 Finding the Difference of Squares Write each expression in expanded form. Use FOIL or the distributive property. Row 1 (x + 5)(x − 5) (b + 2)(b − 2) (y + 6)(y − 6) ____________________ _____________________ _______________________ ____________________ _____________________ _______________________ 1. What pattern do you see in the answers from Row 1? ____________________________________ _________________________________________________________________________________ 2. What happens to the two middle terms in these types of expressions? _______________________ _________________________________________________________________________________ 3. Can you use that pattern to predict the expanded form of (x + 3)(x − 3) ? _____________________ _________________________________________________________________________________ The difference of squares means you’re taking two binomials with the exact same terms, but you’re adding one pair of terms and subtracting the other pair of terms. The expression (x + 6)(x-6) is an example of the difference of squares. Remember, difference simply means the answer to a subtraction problem. The reason these expressions are referred to as the difference of squares is because the expanded form ends up being the first term squared minus the second term squared. Rule The Difference of Squares (a + b)(a − b) = a 2 − b 2 (x + 3)(x − 3) = x 2 − 3x + 3x − 9 = x 2 − 9 (3x + 4)(3x − 4) = 9x 2 −12x +12x −16 = 9x 2 −16 Multiplying the sum and difference of the exact same two terms will always give a product called the difference of squares—the first term squared minus the second term squared. Example Write each expression in expanded form. Use FOIL or the distributive property. (x + 5)(x − 5) Original equation 2 x − 5x + 5x − 25 Distribute (x+5) x 2 − 25 Combine like terms
- 2. CHALLENGE 11 DIFFERENCES OF SQUARES 2 In challenge 5, we talked about square lots -‐ 2 that were changed into rectangles by adding 2 meters to one side and Square lot Rectangular subtracting two meters from the other lot side. The factored form of this expression x x was written as (x+2)(x-2) x x + 2 4. Is the expression (x+2)(x-2) a difference of squares? How do you know? _____________________ _________________________________________________________________________________ 5. What were the differences in area for any number we put in for x? (Hint: If you don’t remember, rewrite (x+2)(x-2) in expanded form. __________________________________________________________ __________________________________________________________________________________ Practice Write each expression in expanded form. Use FOIL or the distributive property. (a + 8)(a − 8) (b − 5)(b + 5) (c + 3)(c − 3) (2d + 6)(2d − 6) (5x + 7)(5x − 7) (10y − 4)(10y + 4)