Compute the following in your head-i 672-332ii 1232-1222iii 5-72-2-72iv 0-272-0-232

We know that x2 − y2 = (x + y) (x − y) (i) 672 − 332 = (67 + 33) (67 − 33) = 100 × 34 = 3400 (ii) 1232 − 1222 = (123 + 122) (123 − 122) = 245 × 1 = 245 ...

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Standard VIII

Mathematics

Addition and Subtraction of Negative Numbers Using Algebra

Compute the f...

Question

Compute the following in your head:

(i) 67² − 33²

(ii) 123² − 122²

(iii)

(iv) 0.27² − 0.23²

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Solution

We know that x² − y² = (x + y) (x − y)

(i)

67²− 33² = (67 + 33) (67 − 33)

= 100 × 34

= 3400

(ii)

123²− 122² = (123 + 122) (123 − 122)

= 245 × 1

= 245

(iii)

(iv)

(0.27)²− (0.23)² = (0.27 + 0.23) (0.27 − 0.23)

= 0.5 × 0.04

= 0.02

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Observe the following pattern:

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Compute the following in your head: (i) 672 − 332 (ii) 1232 − 1222 (iii) (iv) 0.272 − 0.232

We know that x2 − y2 = (x + y) (x − y) (i) 672 − 332 = (67 + 33) (67 − 33) = 100 × 34 = 3400 (ii) 1232 − 1222 = (123 + 122) (123 − 122) = 245 × 1 = 245 (iii) (iv) (0.27)2 − (0.23)2 = (0.27 + 0.23) (0.27 − 0.23) = 0.5 × 0.04 = 0.02

Compute the following in your head:

(i) 67² − 33²

(ii) 123² − 122²

(iii)

(iv) 0.27² − 0.23²

We know that x² − y² = (x + y) (x − y)

(i)

67²− 33² = (67 + 33) (67 − 33)

= 100 × 34

= 3400

(ii)

123²− 122² = (123 + 122) (123 − 122)

= 245 × 1

= 245

(iii)

(iv)

(0.27)²− (0.23)² = (0.27 + 0.23) (0.27 − 0.23)

= 0.5 × 0.04

= 0.02