Formulas

Demonstrate a 2 + 2ab + b 2 = (a + b) 2 Find the area of the big square by adding up the areas of the 2 squares and 2 rectangles: a 2 + ab + ab+ b 2 = a 2 + 2ab + b 2 Is there another way to find the area of the big square? Yes, the side of the big square is (a + b) so the area is (a + b) 2 a a b b a2a2 b2b2 ab a + b a a b b

Demonstrate a 2 - b 2 = (a + b) (a - b) Take the big square and cut off the small square on the left corner a 2 - b 2 Calculate the rest of the area by re-arrange the pieces left and make a new rectangle: The new rectangle has the area (a + b) (a – b) a b b b a a a - b