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Learn how to identify and expand the three special products in math. This lesson covers the square of a sum, square of a difference, and difference of squares.
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9-8 Special Products Objective: To identify and expand the three special products
Today we are going to learn… • 3 Special products: • Remember: products means we’re multiplying • They are special because we can use them as shortcuts • The box method will still work
SQUARE OF A SUM a2 + 2ab + b2 a + b a + b a b a a2 ab b2 b ab (a + b)2 = ( )( ) =
Multiply (2a + 3)2 4a2 – 9 4a2 + 9 4a2 + 36a + 9 4a2 + 12a + 9
SQUARE OF A DIFFERENCE a – b a – b a2 – 2ab + b2 a -b a a2 -ab b2 -b -ab (a – b)2 = ( )( ) =
Multiply (x – y)2 x2 + 2xy + y2 x2 – 2xy + y2 x2 + y2 x2 – y2
DIFFERENCE OF SQUARES a2 – b2 a b a a2 ab -b2 -b -ab (a + b)(a – b) =
Multiply (4m – 3n)(4m + 3n) 16m2 – 9n2 16m2 + 9n2 16m2 – 24mn - 9n2 16m2 + 24mn + 9n2
EXAMPLES x2 – 12x + 36 9p2 + 24p + 16 9 – 25x4 1) (x – 6)2 2) (3p + 4)2 3) (3 – 5x2)(3 + 5x2)
EXAMPLES 4) (4a – 3b)2 16a2 – 24ab + 9b2 5) (m + 5)2 m2 + 10m + 25 6) (8a – 7b)(8a + 7b) 64a2 – 49b2 7) (6c + 10)(6c – 10) 36c2 – 100
Homework • 9-8 Practice
