Question

Part 1. Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)2 = x2 − 2xy + y2 to square your number without using a calculator.Part 2. Choose two values, a and b, each between 8 and 15. Show how to use the identity a3 + b3 = (a + b)(a2 − ab + b2) to calculate the sum of the cubes of your numbers without using a calculator.

Answer 1

Solution:-1

Number be 27

$\\ \sf\longmapsto 27^2$

$\\ \sf\longmapsto (30-3)^2$

$\\ \sf\longmapsto 30^2-2(30)(3)+3^2$

$\\ \sf\longmapsto 900-180+9$

$\\ \sf\longmapsto 909-180$

$\\ \sf\longmapsto 729$

$\\ \sf\longmapsto 27^2$

Hence verified

Solution:-2

• a be 10
• b be 9

$\\ \sf\longmapsto 10^3+9^3$

$\\ \sf\longmapsto (10+9)(10^2-10\times 9+9^2)$

$\\ \sf\longmapsto 19(100-90+81)$

$\\ \sf\longmapsto 19\times 91$

$\\ \sf\longmapsto 1729$