Use Identity 1C to calculate 98 × 102, and 45 × 55. Class 8

Use Identity 1C to calculate 98 × 102, and 45 × 55. Class 8

Question 1.

Use Identity 1C to calculate 98 × 102, and 45 × 55. Class 8

Solution:

98 × 102 = (100 - 2) (100 + 2)

= 100² - 2² = 10000 - 4

= 9996.

45 × 55 = (50 - 5) (50 + 5) = 50² - 5²

= 2500 - 25 = 2475

Question 2.

Which is greater: (a - b)² or (b - a)²? Justify your answer.

Solution:

Both are equal to a² - 2ab + b².

Question 3.

Express 100 as the difference of two squares.

Solution:

[latex]\left(\frac{50}{3}\right)^2-\left(\frac{40}{3}\right)^2[/latex] = 100.