Question

Simplify 105 X 92 using algebraic identity with explanation .​

Answer 1

Given :

• 105 × 92

To Find :

• Simplify 105 X 92 using algebraic identity with explanation.

Identity Used :

• (x + a) (x + b) = x² + (a + b)x + ab

Solution :

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 = 9660

Therefore :

• The required answer is 9660

More Identities :

• (x + y)² = x² + 2xy + y²
• (x - y)² = x² - 2xy + y²
• x² + y² = (x + y) (x - y)
• (x + a) (x + b) = x² + (a + b)x + ab

━━━━━━━━━━━━━━━━━━━━━━━━