Saved Bookmarks
| 1. |
Simplify 105 X 92 using algebraic identity with explanation . |
|
Answer» 105 × 92To Find :Simplify 105 X 92 using algebraic identity with explanation.Identity Used :(x + a) (x + b) = x² + (a + b)x + abSolution :To use the identity we have to break 105 and 92 in the form of (x + a) and (x + b) where x should be common. So we can write 105 as 100 + 5 where 100 stands for x and 5 stands for y. Similarly 92 can be WRITTEN as 100 - 8 where 100 stands for x and -8 stands for b. Now we have got x as common (i.e 100) so we can APPLY the identity now. ⟶⠀(x + a) (x + b) = x² + (a + b)x + ab⟶⠀105 × 92 = (100 + 5) (100 - 8)⟶⠀105 × 92 = 100² + (5 - 8)100 + 5 ×(-8)⟶⠀105 × 92 = 100² + (-3)100 - 40⟶⠀105 × 92 = 100² + (-300) - 40⟶⠀105 × 92 = 100² - 300 - 40⟶⠀105 × 92 = 100² - 340⟶⠀105 × 92 = 10000 - 340⟶⠀105 × 92 = 9660Therefore :The required answer is 9660More IDENTITIES : (x + y)² = x² + 2xy + y²(x - y)² = x² - 2xy + y²x² + y² = (x + y) (x - y) (x + a) (x + b) = x² + (a + b)x + ab━━━━━━━━━━━━━━━━━━━━━━━━ |
|