Square of the Difference of Two Numbers

Transcript

Square of the Difference of Two NumbersWe have an Identity Let’s do an example of this The area of a square of sidelength 60 units is 3600 sq. units (602) and that of a square of sidelength 5 units is 25 sq. units (52). Can we use this to find the area of a square of sidelength 55 units? We can split our square of length 55 into 4 parts A square of length 60 A square of length 5 Two rectangles – 5 × 60 and 60 × 5 Here, we basically subtract, 55 = 60 – 5 Let’s look at it visually We can get the area of the square of sidelength 55 by Taking the area of the square of sidelength 60 And removing the areas of the two rectangles of sidelengths 60 and 5, i.e., 602 – (60 × 5) – (5 × 60).By doing this, we remove the area of the small square of sidelength 5 twice. So, we add 52 again Thus, 552 = (60 – 5)2 = 602 – 5 × 60 + 60 × 5 + 52 = 602 – 5 × 60 + 5 × 60 + 52 = 602 – 2 × 5 × 60 + 52 = 3600 – 600 + 25 = 3025 Now, let’s do an example Example: We divide 102 into different parts, but get the same area Here, 102 = (8 + 2)2 And, 102 = (3 + 7)2 Both areas is same Now, let’s do some questions